Yes, FX glass works on a DX camera. It works really well actually because it's not using the outside edges of the lens where any imperfections are typically located. 100% of a DX sensor will be looking at the "sweet" spot of the lens. (Very simple explanation)
"Good" glass on an "ok" body is better than "ok" glass on a "good" body. I wouldn't even be having this discussion if I didn't have some good deals lined up on a used D7000 or a D700. Plus, investing in FX glass now makes the jump to FX body later on much easier. In my scenario right now, I really should buy some FX glass too if I went to a 700/600, unfortunately that's not in the cards right now.