Can center speaker glare affect picture contrast?

For the person it bothers, it might drive them crazy..
Once you start noticing the reflection in the black gloss, and dwell on it all the time, I guess it would constitute a PITA situation.
If you sit low enough to not notice the reflection of the screen in the gloss finish, then no it will not matter. Nor will it matter if you just ignore the issue.
The 'problem' is for those for whom it would drive them nuts.
My center channel has a metal mesh front, and I painted it flat black to avoid it attracting attention in general.. Even though the other four are still silver.
PS if it bothers you, you could just place a black cloth over the top while watching. or spray the top only with a flat finish clearcoat, or,double sided tape a black paper to the top of the speaker. The black paper would be no glare.

I have about the same clearance above my center channel. (119 in Da-Lite, and Sony PJ) I use a gloss black center. I really don't think it's an issue. When you dial in the PJ, to fit the screen, there really shouldn't be any direct light from it hitting the top of the speaker. What you do see on it is reflecting back off the screen, towards you, which shouldn't effect your picture.

It wont be an issue, even if it was place black velvet cloth on top so you get both look you want and a cure for a doubtful issue.

Thanks for the feedback. Went ahead and got the black gloss finish.