how cheap is cheap? like eastwood cheap,$800ish dollars? or cheap as in $200? ive used the eastwood tig, and its OK, not bad, not great but probably one of the better "cheap" chinese ones i suppose, although the only thing i could think of while using it was how it felt "toy-like". i have no idea what your skill level is, but if its beginner in tig, i feel like it could make it harder to learn on.
my main issue with buying a no name brand off ebay would be serviceability. if you buy it for X amount, and theres an issue a month or 2 down the road, how easy is it going to be to get it back up and running if it at all and how much more money is it going to cost to fix. im well aware there are quality chinese products, but if you cant get a replacement part or a consumable part, its sort of a moot point.
local welding supply houses and craigslist can be a good source for a quality used machine. cost might be a little higher but, the possibility of it costing you less in the end it pretty good, and you get to actually handle the machine before buying it