I just put microfiber on the back of my nine-patch and so far, it seems to be holding up okay, but I sort of regretted the decision to do it. There was a lot more lint than I was ready for when I stitched on the binding and quilting cat is right, getting a needle through to tie it was unbelievably difficult and my hands suffered for a couple of days. Add to it that there were a couple of times I broke one thread when I was trying to push the needle through and there are now a couple of runs I'm going to have to watch closely to make sure everything doesn't fall apart.
Microfiber is great for a lot of things, but putting it on the back of a quilt, I would have to say no.