I would be concerned about the long term outcome of this experiment. In particular I'm worried that eventually the glue would weaken and the protector would pucker/lift upward in the middle of the playfield. Poly-carbonate expands at a much greater rate than wood when heated.
I made my own protector for a Bally Quarterback. Instead of cutting around all of the playfield posts, I used small holes that went underneath all of the posts and reinstalled the posts on top of the protector. I quickly learned why the protectors were designed to go around all of the posts: to allow for expansion. Within minutes of turning the game on, the protector lifted away from the playfield in the middle by at least a quarter inch! This wildly changed the direction the ball moved in during the game. After turning the game off and letting it cool, the protector sat back down as flat as could be.
I thought about gluing it down, but my solution for this problem was to make sure the game/playfield never heated up. Obviously the first step was to replace every bulb in the entire machine with single LED bulbs. Next I noticed that there was a bridge rectifier installed on the bottom of the playfield using the playfield as a heat sink. I unscrewed the rectifier and attached it to a metal heatsink installed on a plastic standoff. After that I unscrewed all of the relays attached to the bottom of the playfield and installed them on plastic standoffs. Finally I installed a forced air cooling system with two 64CFM fans blowing in through the bottom of the machine where the coin box once was. The air blows directly toward the flippers then passes along the playfield and out the top of the backbox. One entrance, one exit. I installed temp probes in the machine and it doesn't heat up more than one degree even after hours of play! The end result is the playfield protector sits flat and plays amazing no matter how long the game is turned on.
My recommendation for anyone who installs this product is to do whatever possible to remove heat from the game and in particular insulate the playfield from heat producing components and boards. I might have gone overboard with the fans, but better safe than sorry. As long as the game does not heat up much during play, there should be nothing to worry about. I look forward to someday trying one of these on one of my machines.