I wondered if a glossy print behind glass would look bad.
So I tested it for myself. Used a Canon Photo Plus Glossy (PP-101) print from a low-end PIXMA, genuine Canon ink. There was a mount between the print and glass, of about 2mm. The image had a lot of uniform black and a chunk of lighter tree bark detail. To be honest, I tried all sorts to get some annoying reflections and really struggled to make it look bad. I had to use an LED torch in the end and hold it at an angle whilst contorting myself to look from another angle,and it wasn't that bad. There was more shine form the glass!
Now, the problem with gloss is that if anything mars the finish before it goes in under the glass, then you could see some yukky surface marks. this definitely won't happen with matte papers, like photo rag and such, and probably less likely with pearl/lustre types too. Baryta may suffer from the potential to mark the surface sheen, but glossy is the worst, because any change in glossy sheen would be so obvious.
We've got Canon Semi-Gloss SG-201 on order. Will be comparing against the Glossy PP-101 and will probably prefer the semi-gloss, which I understand ain't much different to the more expensive Lustre, and the ICC profiles are the same.