Absolutely! It's up to you, what it will affect is the weight of the quilt.
I just finished a rag quilt where both front and back are flannel, I put smaller flannel squares in the middle of the 2 larger squares and it's really heavy (my outside squares are 8-1/2" and there are 200 of them, 100 on each side). If I do another one, I'm leaving out the middle square.
I've made these out of fleece too and I don't put a middle square between the fleece squares because of the added weight.
I teach sewing and my students have made rag quilts with smaller squares, with center squares, out of flannel and they haven't been as heavy so the center square works well and probably adds warmth.
Whether I'm adding an inside square of not, I always sew an X on the 2 squares I'm joining together.
When I'm done "ragging" the quilt, I put it in my washing machine on a rinse and spin cycle, then I toss it in the dryer on high heat. I set a timer for 10 minutes and stop the dryer every 10 minutes and clean out the lint trap until very little lint is appearing in the lint trap.
Here's a couple of great sites with really good pictures on the technique that may also help.
http://greenappleorchard.blogspot.co...-tutorial.html
http://www.lovetosew.com/ragquilt.htm
http://jenyu.net/make/ragquilt.php