Yes. But why not get a US psu for the A1200?
Exactly. Buy a junk A500 in the US, and use its power supply. That's a cheap and easy upgrade, plus no nasty voltage conversion. ;-)
Running a computer on a voltage computer should only be considered a very last resort. Computers are very sensitive to power fluctuations, and most (cheap - i.e. less than the price of a dirty A500) voltage converters are crap at supplying steady, clean power.