Sure, I do it all the time, especially for kids quilts.
I usually use a piece of flannel for batting so it won't be so thick. But I've done it without batting also. Your stitches can get lost in the fleece so you might want to lengthen your stitch. Machine quilting right? I wouldn't try hand quilting with this.
You're binding can be a problem also. You can make a wider binding, to help with the thickness, you can fold the fleece backing over to the front and not use a separate batting, or once I put that wide satiny baby binding on with a zigzig stitch, fast!! and looked great!!
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