I took a photo of the two blocks so you could see the difference. The one on the left was stitched with stabilizer. It is still really flat. The one on the right was stitched without stabilizer and you can see that it has a more ripply texture around the stitching. It turned out okay, probably because each fabric was spray starched to death beforehand.
I was curious what the difference would be when I had ripped off all the stabilizer (I use Rinsaway by HTC, but you have to tear it off). I use a seam ripper (carefully) or a ball-point awl (couldn't find it today) to help rip the pesky inner points of stabilizer.
The picture below shows the same two blocks after ripping. The one on the left still has stabilizer behind the dark gray, I don't rip that part off. The one on the right has no stabilizer at all and is clearly more ripply. In the long run, both of these blocks are going to work fine, but I was definitely happier with the stabilized block.