I ride a hardtail, and I wonder if a full suspension prevents pinch flats in the rear wheel. I don't get pinch flats; but I want to know what to expect from a hardtail vs full suspension. I'm a heavy man (100 kgs) and like to go fast (60+ k/h) in bad dirt roads (not downhill), and my main worry is getting a pinch flat (or blow out). I use 40 psi in my rear wheel (26x2.10).
Full suspension will not, by itself, prevent pinch flats. Since pinch flats are something that occur from the way the tire and tube move in regards to the rim, adding suspension won't change that. Now, adding suspension could move some of the pressure forward, depending on the pivots are arranged.
If you're riding at 40psi on a 2.10 tire, you should be fine on just dirt roads; however, if you hit a really nice square edged pot hot at that speed you're probably going to flat on either type of bike. Preventing pinch flats is usually more about tire pressure and deformation of the tire than anything else.
Honestly this has more to do with how you let your bike "float" underneath you over obstructions than it does with rear suspension or the lack thereof. Since you can potentially go faster on a full suspension over rough terrain than you can on a hardtail I would say you're just as likely to get pinch flats. You just have to unweight the back of the bike and stay loose as you cross rocks/roots/whatever. That's a crucial key not only in reducing pinch flats, but in going faster over technical terrain as well.
Short answer, just as likely on either platform depending on your riding style.