In theory, yes. But, I have to ask, have you quilted anything on it yet? Even a length of practice fabric/batting/backing? My thought is that I would want to make sure I've got the nuts and bolts down, making sure everything is running smoothly with my newly set up machine. Then, do any of your friends have a quilt they'd like you to do for them? You can test some more...
I'm not a pro, by any means, but I have used a long arm for several quilts over the past year+. Let's think this through a bit.
There could be some potential issues with the pre-sandwiched, glued quilts, I would imagine. #1- were the quilts sandwiched from the center out, or at least carefully layered so as to not stretch the fabrics and create bubbles and creases? If they're pretty flat, and you don't load too taut or too loose, it could work. But, you do risk stitching puckers into the quilt. #2-How much glue did you use? Could there be an issue of buildup on the needle that might cause drag on the thread and possible breakage as you quilt?
#3-Is there a possibility you could soak the quilts to separate the layers? (I say with a little squint and a cringe...LOL)