I have not used micro fibre but I have backed a wool wall hanging with thick wool. I have to use big stitches to quilt as it difficult and a thimble with my needle to do the binding. It is not something I would want to do again but I got it done.
If it is a lap quilt I say give it a try. If it is queen size, I probably wouldn’t . You didn’t mention if you are machine quilting it on a sewing machine or longarm. If you have a long arm, I imagine it would quilt similar to milky which some of our long armers like doing.