Oh, duh! Haven't had enough coffee today, I guess. I've worked with fleece but never used liquid stitch on it. I still wouldn't trust it for a seam without making a test seam to see how it would hold up to stress. It would probably work well to hold down the seam edges after sewing, though. I have always used a small zigzag to sew seams in fleece. This is because fleece is stretchy and the small zigzag will stretch with the fabric; a straight stitch will be more likely to break if the fleece is stretched (say, by a little girl sitting down on it).
I should add that, for this particular application, I'd probably be inclined to overlap and do a fairly wide and long zigzag stitch on each side. You could try it out on a test strip to make sure it would look okay.
HTH more than my previous comments! :P