Haven't tried it, but I don't think it would damage anything. Most thermal pastes I've dealt with are silicone greases, with various particles added for thermal conductivity.
However, I'm not sure it would make much difference in heat transfer. Thermal paste by itself isn't a great conductor of heat; it's just a lot better than an air gap. When installing a CPU heatsink, the idea is to get a very thin, even layer of compound between the chip and sink - the compound fills in the gaps at a microscopic level. Most assemblies have a spring clip or some other method of applying force to the junction, to keep them together and squeeze out any excess.
This is also why modders and overclockers will lap their heatsinks (and sometimes, the chips themselves) with very fine abrasives, to get them as flat and smooth as possible. This allows them to use less thermal compound, and get better heat transfer rates.
I'd think that for the distances in a threaded assembly, you wouldn't see much improvement with a thermal compound over a standard thread lube. Threads have to have some play in them, or else they tend to bind or gall when tightened, even with lube.
Of course, this is all conjecture, and I don't think using thermal compound would hurt anything, so somebody give it a shot and see.
Jon