Might operating a 50Hz unit at 60Hz affect sound?

What country are you moving to? Most of the rest of the world is 220v/50Hz. Running a 60Hz transformer at 50Hz may run a little warmer, as there is less reactance - therefore more current in the primary. But if your components are voltage-switchable (or you get the transformers changed) this wouldn't matter. Probably can disregard the 50/60hz thing anyway. (except on some turntables which require the proper frequency for the motor).

I would say it probably be ok as long as the Voltage is correct. Also, here's another consideration. When you get to Argentina, your fuses might be too 'big'. Lets say your amp has a 4 Amp fuse for the US. You will need a 2 Amp fuse for 220V because while the voltage is doubled, the current is halved. Check your owners manual for proper fuse size with 220V.

Same thing happened to me, but in reverse. I bought a cheap Chinese tube amp that was dual voltage but was fused for 220V (at half the current as stated above). So when I turned it on, it blew the fuse. I just got a twice-bigger fuse and it worked fine. (Remember you have the Opposite situation - you wont blow fuses, but you won't have the proper protection with a too 'big' of a fuse.

Again, check the owners manual - because it may override what I said, which is usually, but not always, true.