It would depend on who did the refurbishing and what the warranty is.
As long as it has a good warranty, at least what you would get with a new one, then I'd say its passed the first test.
Then, if it's factory refurbished, I think you're good to go. But, if it's camera shop refurbished, I'd vote no.
At least if the factory has done the work, you can be reasonably assured that it was done right and the it's likely the only thing that might be wrong with the camera is cosmetic. On the other hand, I don't know that I'd trust the camera shop to do the work.
In the end, if you have a warranty you're covered regardless of who did the work of course. But ask yourself if you really want to have to exercise the warranty...I know I'd rather get the manufacturer refurbished unit so that likelihood is minimized.
Good luck with your purchase decision.
And out of curiosity, what camera are you looking to get?