Yes, you can use fleece as bedding. I do.
I sew with the stuff and sell things as Chucklebunnies, but tend to use furnishing fabrics for tunnels and fabrics that are lighter and will gather to make round pillows. There's instructions for how to make a round pillow on the thread 'DIY for piggies' and I'm happy to give further instructions if you like but I wouldn't use fleece for it. Fleece is good for homes with stiffened openings or cuddling pockets and lap blankets. I have used it for tunnels, it is possible and very washable, but not the best stuff!
Piggies like to stretch out on fleece - nice and soft - so a loosely stuffed rectangular pillow that's long enough for them to stretch out on would be used well. Loosely stuffed so that they can snuggle down into it, they prefer that to lying draped over an overstuffed one. Use more stuffing around the edges with a retaining seam to make a higher layer around the edge if you can and never leave hand sewing visible or they'll pull the stitches and eat the thread!
Easiest way to do it - two pieces of fleece four inches longer than your piggie and three inches wider. Sew mostly closed, turn the other way out to hide the seams, stuff loosely and finish neatly on the machine. For the edge - make a roll of fleece stuffed like a long sausage and then machine this to the pillow, using the pillow fabric to sew with, rolled up onto the sausage fabric. This is the tricky part and may be where it goes wrong...some skill is required. The sausage must be loosely stuffed at the corner bits but you can usually push the stuffing around as you sew it. Best of luck. If you have to attach the sausage by hand - your machine may not cope anyway, then just put the hand sewing on the bottom so your piggies don't eat it. This would make a generously sized pillow with a raised edge that they would be happy to lie on.
Hope that bit of advice helped...
Sarah x