I didn't used to be as careful with making sure borders squared before starting to long arm--now I am! I try to make sure that the quilt is square (not more than 1/4" and hopefully less) before I put on the borders. And remember that each border that you put onto an unsquare quilt, the more unsquare the end result. Acutally, I try to remember and take the time to square each block as I go, too.
One thing that' I'd suggest is that you let your long arm quilter know if there is any problems when you give it to her/him. Talk with them about your concerns so that can be considered when planning the design. A really wavy border may force the long armer to make a tuck(that would look like a straight seamed border)to prevent puckers.