I'm sure you would not be the first to use fleece. But it is more expensive than traditional batting. I'm a bit surprised you're not planning to use it as the backing itself. Here are some thoughts that might help you.
On the "pro" side:
1. Fleece will last forever! Probably longer than the top and backing.
2. It comes in colors. ( sometimes quilters like to place a thin white cotton over brightly colored fleece creating a colored shadow effect which can be quite pretty.)
3. You may have scraps laying around. If you "piece" it be sure all the pieces are going the same way.
4. It is warm.
5. It does feel nice - "cushiony" - similar to the foam blankets. In fact I've seen people put scraps of those inside quilts. But they can be very "sweaty" as they do not breathe.
On the "con" side:
1. It is more expensive than batting.
2. It is knit and you mustn't stretch it too much during construction or it can pull the quilt askew. Just carefully lay it between the front and back and don't pin and stretch it if you're using a long-arm.
3. If you're "tying" it it might be hard to pull the needle through. Be sure to use a big, pointed needle to open up the hole for the yarn, or etc.
4. It is not absorbent. There is a new "micro-fiber" that is very absorbent, but I don't believe it is available as Fleece. It is used for some minkee.
I hope this will help you in your decision. If it were me, Well, I probably wouldn't use it unless I wanted the shadow effect, and That's something I've been excited to try.
Best of Luck, Judy Lyon