There are no quilt police... the only police I know of try to stop me from getting to work on time
If you are doing an all cotton crazy quilt, quilting it should present no problems. It is when you start including the velvets, silks etc. that problems might crop up. If in doubt, make a test sandwich. They make great kitty parking spots.
BTW the kitty avatar is my cat Binky, who was a foundling. or should I say that we were foundlings, found by her.