That will probably change the performance a little, but I can't remember exactly how.
For the two traps I built, I just split the plastic bag the acoutic sheets came in in half and used that as a backing to keep the glass in.
By the way, now that you have gone through your fabric adventure, muslin is very acoustically transparent and inexpensive. I don't know if you can find it in black though.
If you want to know how the plywood backing will affect your trap, check out the
Home Audio Acoustics forum at hometheatershack.com. The guy who moderates it and answers most of the questions does room treatments for a living and is very knowledgeable.
