yes you can do it. sometimes it makes it a little harder to handle on your home machine, since you have already cut off the extra length on the sides for your binding, but it will not ruin the quilt.
you may want to look up how to bury your threads, since you do not have the edges of the quilt to run your stitches off to. it just helps things look cleaner instead of having thread build up at the binding edge, for example, because you had to start and stop.
Hope that makes sense!