What do you mean that they're stitched on? Are they just secured around the edge, or also through the middle?
I haven't done exactly what you're asking, but I have quilted most of a quilt, then taken it off the frame and turned it around to quilt borders or sashing horizontally rather than vertically. I have also returned a quilt to the frame when I realized that I had missed a spot. If the whole quilt sandwich is well secured, that is very possible. However if you have just stitched around the edges of the quilt, then the whole quilt sandwich could (and probably would) creep as it's quilted on the longarm. You might be better able to avoid this on a dsm.
In this case, if you're sure you don't want to quilt it yourself, you should probably talk to the longarmer who will be doing the quilting. She might want you to take the whole thing apart (which actually isn't as time consuming as it sounds) or she might be able to work with it.