You use a hammock as a bed in ordinary life?? . . . Do go on.
The closest I have come to seeing someone do this was camping next to a guy who slept on an army cot under jungle netting for the whole week in 2008--a very stormy year--with his pick-up truck as a windblock. He was a tough nut; a construction worker. Great guy. I never saw him in a mask (sometimes a bandanna, though) I don't know how his lungs or nose fared. He was bald, which meant he looked less ragged than most people would after sleeping with that level of exposure. He also had a contingency plan--a hard canopy on his truck and could've slept inside if necessary (he might've, but I never saw him do it).
If in doubt, calculate the size of your monkey hut, and buy a smaller dome tent and some 10 inch stakes and leave them in their packages. Keep the receipt. Return afterwards when unused. Having a backup plan--whether it's a boxed tent or a covered truck bed--would be smart. A tent helps keep some of the dust out of you. Not all, but probably reduces it by half. That's a guess.
Also, I don't know what kind of hammock you mean, but if it's freestanding, you can put it in a tent, of course. You'd want to take your measurements really carefully and take into account the height at which the walls of the tent start to pitch inward so you'd be sure you could get the hammock in there.
ETA: If you decide to go without a tent, make sure your sleeping bag is rated to keep you alive at 40F or colder, and bring some fleece jammies and sleep socks. Tents, as thin as they are, do give you a little bit of warmth. My friend who slept outside was not doing it on a particularly cold year, as stormy as it was. The coldest I remember feeling was about 50F. Occasionally it can be in the mid to high 30's in the wee small hours (2010 was like that on several nights).
*** 2013 Survival Guide ***
"I must've lost it when I was twerking at the trash fence." -- BBadger
"Snark away, ePlaya, you magnificent bastards." -- McStrangle