Can I use microwave turntable glass plate in convection mode?
Assuming you do not have access to the instruction manual, and/or the manual does not specify whether it is safe to use the glass in convection/grill mode, I would assume not.

Are there any labels and/or writing embossed on the glass?

As I described in this similar question, "regular" soda-lime glass is not heat safe.  Given that the glass was obviously designed for a microwave, it is probably tempered glass, so it can withstand some amount of heat.  Therefore, I would treat it like a Pyrex baking dish and not heat it to over 500°F.  Your microwave's convection mode likely does not get that hot, so you are probably fine with that, but no guarantees.  I would not use the tray in grill mode because even Pyrex is not broiler-safe.