A lot depends on how far apart your ties will be. They need to be closer together than whatever the batting specifies as quilting distance. For example, if Warm and Naturals specifies quilting lines need to be 10" apart, I would place ties so that no tie is more than 5" away from another tie. The reason ties need to be closer is because they are single points of contact for all three layers; with quilting, the stitches are creating many more points of contact.
I would probably prefer poly batting for a tied quilt simply because it is puffier, plus its lighter weight means there is less stress placed on each tie point. However, if you don't place ties sufficiently close together, any batting will ball up inside the quilt eventually -- mostly from being machine washed and dried.