depending on the converter you may lose AF ...
also a 2x will reduce your f stop by 2 stops, a 1.4 by 1.4 and a 1.7 by 1.7.
It's certainly a cheaper option than going for a 600mm f4.
1.4x loses one stop of light.
By Lynton's maths a 1x (no change) will lose one stop.
He is dead right about losing AF. Two reasons.
1) The teleconverter may not support it. Beware of eBay 'bargains'.
2) Using your f5.6 with the 1.4TC gives an effective aperture of f8. You camera will not focus at f8; nor will any of mine. 'Taping the pins' to spoof the camera produces awful results that have never worked for me.
There's also the little matter that not all lenses are compatible with teleconverters; you gotta check they are compatible before buying.
Note: different manufacturers teleconverters have difference compatibility lists; if the Kenko is compatible, don't assume the Canon is, and vice versa, etc.
In my early days I bought a 2xTC for use on my 70-200 f4 without checking the forums - it was compatible but AF did not work and it has sat in the cupboard for years. It is finally getting some proper use now I have a 135mm f2, but it was a bad purchase.
In summary - a 600mm f4 may be a lot of money, but that's better than wasting money on a TC that you cannot use.
How about a used 100-400 ?