50Hz or 60Hz? If it's 220V, 60Hz to a transformer, the transformer shouldn't care where ground is. Only if they did something peculiar like connect the transformer neutral to ground (which is _not_ kosher by current US standards) would you have a problem.
If you have 50Hz AC out there and the transformer was designed for 60Hz then it may not have enough turns to work right -- your magnetizing current will be higher and you may saturate your core. Your best three bets are to (a) look at the nameplate on the transformer and see what it says, (b) plug it in and check the current going into the transformer at idle, see if it's less than 10% of rated current, and if it passes (b), plug it in for a while and see if things get too hot.
I suspect that even if it's not specifically designed for 50Hz operation that as long as you don't keep the transformer energized for too long at a stretch (i.e., use it then TURN IT OFF), you'll be fine. But don't take me to court if I'm wrong!!
Ditto the Granger spot welder, if it can be rewired for 220V you should be fine if the frequencies match up.