Yep. The thing that matters for respiration is oxygen partial pressure. On the Earth's surface, your body gets about 2.9 psi of oxygen mixed with nitrogen and whatnot...
I bet that a very low-grade pressure suit----a handful of rubber straps around the chest, at the level that'd make it difficult to inhale on Earth---would take a lot of the load off of breathing. Maybe you could get up to 1.0 or 1.2 psi.
Good post. A couple of additional details, though:
The effective suit pressure is a little bit higher because of two practical concerns. First is that there will also be a vapor pressure -- your own aspiration will displace some of the oxygen as you lose water into the super-dry tank air. Second is that there is some additional minimum operating pressure in your lungs.
So the actual minimum pressure for a 100% oxygen mix in a spacesuit works out to be a shade over 4 PSI, if we're delivering the same amount of oxygen as we're used to. If we're running at the ragged edge and don't mind blacking out, 3 PSI might be survivable.
Pure oxygen is rather dangerous and uncomfortable, however. Most spacesuits contain some inert gas in the mix, albeit not much since you have to carry it all with you. The A7L suits used in Apollo ran at about 5-6 PSI, running about 80% oxygen and 20% nitrogen. Yes, nitrogen -- unlike deep sea diving, there's no reason not to keep nitrogen in your system instead of flushing with helium. If you decompress, the bends will be the least of your worries...
Running at low pressure in a spacesuit helps in a few ways, one being it makes the suit less prone to bursting, another that it lightens the tanks. But some space applications are much closer to a "shirt-sleeve" environment. The International Space Station runs at full sea level pressure. This cuts down on the risk of fire, makes working more efficient, and provides some added protection from radiation.
It isn't clear what mix we'd use on Mars. I suspect it will be closer to the high pressure mix used on Station, but it's a complicated decision.