Pretty much all the trips listed in my sig. have been 2WD possible. Sure it might have included some getting stuck and needing a pull out but that happens to pretty much any truck that goes off-roading, regardless of 2WD or 4WD. We all get stuck at some stage.
If you ask people who are arranging a trip, they will usually advise you if 2WD is cool or not.
So in short...SURE.
Our trip to Pismo last weekend was cool (temp.) and there were two trucks with 2WD. They did really well. In the dunes it's more about tire inflation and momentum.
I think there might be a trip to Anza Borrego before the end of the year. Keep ya eyes on the regional forum for details. You should check out Big Bear. There's lots of trails there that are 2WD.