If you are running beadlocked rims with very low psi, is the tire more susceptible to damage?
Sure, you've got the sidewall flexing a lot and more susceptible to rips and punctures. However, that is why there really is no "magical" recommendation as to tire pressures in that it depends on variables such as vehicle weight, terrain, and the tires themselves.
Starting with the tires, some makes and brands are known to have more puncture/tear proof sidewalls than others. Without getting into a debate over specific brand and model of tires it is pretty easy to ask around and get an idea of a tires reputation for withstanding sidewall damage. If low psi wheeling is in your plans look for heavier multi-ply sidewalls or plys of special materials like Kevlar. Also think about "load range." While having a stiffer (maybe too stiff for extremely light vehicles) sidewall, load range D or E tires may perform better than load range C tires in some situations.
Obviously, soft surfaces like sand, dirt and mud are going to be more forgiving to the tire than crawling over glass-like shale, volcanic rock, or gumbo-mud strewn with sharp sticks and debris.
So while the simple answer is "yes" to your question can low psi can make tires more susceptible to damage, it really comes down to having the right tires for the kind of wheeling you do and having the familiarity with your rig and experience to know how and when to vary the amount of tire pressure you run.
Since 2003, I'm on my 3rd set of Goodyear MT/R's (this last set with Kevlar in the sidewalls) and have yet to use my Safety Seal Off Road tire repair kit. I've loaned it out to others but have yet to punch a hole in my own tires. That either says a lot for the durability of the tires or the fact that they keep Mall parking lots so hazard-free, or hell, maybe I've just been lucky.