I think that fleece would make a super soft backing - but - I think it will be very stretchy and very slippery to sew!!
I was just having a look at them @Lowena. Home Bargains has one direction fleece. Fleece that goes in one direction?, I thought. No it was this. https://www.homebargains.co.uk/products/7662-one-direction-fleece-blanket.aspxMaybe not!
I would expect ordinary polartec-type fleece to be easy to quilt, but I think the one Pearl is looking at is one of those with a longer velvety pile which could fight back!