I'm not a natural fiber fanatic either. I don't like ironing clothing.
I wouldnt' try to hand quilt poly quilts - tie them. They are kind of stretchy for machine quilting, but you could try.
I have made a LOT of them as charity quilts for orphanages, nursing homes, hospitals, fire depts, etc. I sew them on the serger.
I'm from Wisconsin, where we LIKE hot heavy quilts. ;)