Short answer is 'No'.
To untangle some of the answers why not, and how not to, though..... There are two main reasons you 'wouldn't' shoot a film at box speed, and they aren't mutually exclusive.
First (and more complicated) reason, and is the one that has been most commented on is
Pull/Push processing.
The Box ASA/ISO is a film's sensitivity for a certain 'standard' processing chemistry, and is a 'suggested' optimum to for the film, hence the 'recommended' speed.
But you can usually shoot a film at up to maybe 3-stops over or under the box speed, and compensate in processing, using different development timings, temperatures, chemical concentrations and or chemicals, for the consequent over or under-exposure.
Most common reason you might want to do this is if you have loaded up with say 100ASA, set the camera to that, then changed film, and forgotten to change the ASA selector, when you loaded say 400ASA; so you get a whole roll of film, that has been two-stops over exposed. Now, under developing the film, can pull that back a bit and stop dev blowing out so many high-lights, or washing out the shadows as badly. This is called 'pull' processing. Wicky-Worky, load 100ASA after having set for 400, you can compensate for the under-exposure, some, by over developing the film, 'Push' processing, to boost the highlights and get some shadow detail back.
Working away from the manufacturer's 'optimum', you would tend to loose 'something', often exposure range, and contrast compared to 'optimal' processing, and usually the grain is effected too, so it's essentially a 'recovery' technique, but can be exploited for other reasons.
Many landscape or portrait photographers would routinely 'pull' process, especially with B&W to reduce grain, and get a 'smoother' tonal range, certainly over the mid-tone range, which it could stretch a bit. Hooligans like me, taking rock-shots, would routinely 'push' process, often with slide... mostly because high ASA film, to get pictures in low light of dark dingy venues, was rare and or expensive! I could get 1600 or 3200ASA fuji, in the early 90's, but it was something daft like £15 a roll, when 400 was less than a fiver! So shooting a roll of 400ASA at 3200ASA and then push-processing 3-stops was an appealing option. Such grossly over developed film tended to deliver very contrasty pictures, and with a lot of heavy grain, but that could add 'mood' and 'atmosphere' to the shot.
So, onto the second reason, usually,
exposure compensation.
With an meter coupled 'automatic exposure' camera, setting the ASA selector set the base line for the camera to choose either the shutter speed or the aperture, depending whether it was an aperture or shutter priority AE camera to balance the exposure against the metered light level to the film speed. But, you might not agree with the camera's metering or it's suggested settings.....
First, in-camera metering was never (and still isn't!) all that reliable or trustworthy. And you have the issue that the meter is based on the assumption of 18% grey 'average light'; so in bright or dim conditions, is likely to offer a reading and hence settings that would under or over expose the picture. With a fully manual camera, you would just reject the meter reading, and take a hand-held meter reading or twenty, or just guess by eye, and decide what 'average' you thought best, rather than the camera did. But, if you had a dedicated AE camera, only real way to over-ride the camera's calculations, and get alternative aperture and shutter settings, was to offer compensation on the ASA selector.
Eg: my beloved little XA2 compact, went with me almost every where for twenty years, and it's in-camera metering and AE system was pretty impressive and incredibly 'good' in an era when a lot of point and press cameras didn't even have a meter, and had fixed shutter and aperture and just relied on film latitude and printing compensation to take care of the matter after the event! It's tiny dimensions were much appreciated taking the thing up mountains with me skiing, but almost all my pictures came out 'dark'. Reason being that a white field of snow, fooled the meter into under-exposure; and without any other way to manually over-ride that meter's exposure assessment was to set the ASA selector to a lower film speed, maybe one or two stops beneath box. Wicky-worky, back to them dark dingy rock venues, camera tended to over-expose, left to it's own devices, so, slipping the ASA selector up a stop or two could pull it back, and would often get the shutter speed up to something high enough to avoid blur.
Slight aside; I also had an Olympus OM10, which, as sold, was a dedicated aperture-priority, meter coupled AE camera. It actually had two stops of exposure compensation marked on the ASA selector dial, for this very reason, as it was the only way to provide any manual over ride compensation to the fully coupled system, unless you bought the 'accessory' manual adapter, to offer full manual shutter speed selection. Perversely I have the accessory manual adapter, but seldom used it, and dialed in compensation or correction on the ASA selector, because It was more convenient, and I only had to twist one knob rather than switch over to manual, then make shutter settings, then back again, and, the 'fooled' AE system gave me the 1/3 stop shutter settings in-between the manual adapter's into the bargain! Which is illustration of it being about knowing your camera, in the cat-skinning scenario, finding what works best for you, not slavishly trying to follow the instructions or dogma.
So, you might, 'shot by shot', use the ASA selector to offer exposure compensation, and for those shots, not shoot at 'box' setting. But, you may, like when going up a mountain or into a dingy rock venue, or many other situations, expect to use the whole film, so compensated, OR you might know that your camera's meter tended to a little over or under exposure, or that your film responded better at a different exposure.
Shooting slide film, it was often advised you under-exposed the film maybe 1/3 or 2/3 of a stop, compared to box speed, in order to saturate colours and preserve high-lights. Mostly because with slide, the original negative is directly viewed or reproduced with little opportunity for compensation of correction in printing, and projected onto a screen with a big bright light-bulb, images would tend to be a bit 'thin'. Gives rise to some pretty curious box speeds on older slide films, like 64ASA or 320ASA, you'd likely struggle to find a camera with an ASA dial actually marked to match! Idea was you'd shoot them at 50ASA or 200ASA setting to 'under expose' for saturation anyway....
But in a similar manner, many landscape or portrait photographers, using B&W might routinely shoot up to a stop under to preserve highlights, or up to a stop over to increase shadow detail, and compensate in printing, or to center the tonal range best where they preffered, rather than the film maker's lab-rats thought 'most' folk would like it.
So, the ultimate answer is that the film speed need never be rigidly adhered to, and frequently wasn't/isn't. It was/is only just a guide.
Push/Pull processing, let's you re-rate the film speed to an alternative to the box, compensating for under or over exposure in development and / or printing, if negative film.
Straight Development, will keep the chemistry at the manufacturers reccomended optimum, but the ASA selector, set away from box, can still be used to offer 'exposure compensation', where meter coupled settings may not be the most apropriate, either because the meter cant always be trusted, or the AE program just doesn't give the settings you think most appropriate.
So two reasons to not rigidly stick to box setting, and they aren't mutually exclusive; you may offer compensation on the ASA selector, AND push or pull process the film.
... So just send the finished film off with no special instructions (or extra charges). Remember, HP5 is "proper" black and white, so commercial processing options are rather more limited and expensive, though home processing options are easier and cheaper. The mahoosive 
