Can I take American equipment to Europe?

That gizmo would be a voltage converter. $9.99 at Walmart.

Probably there's an audiophile voltage converter that will cost 10 x as much, and do exactly the same.

there will be no difference in sound, but no doubt someone will come up with some reason why it would sound different.

You need a heavy duty step down transformer that will be able to handle the power required for your system. I personally would not trust the cheap travel converters to be used on expensive audio equipment.

There is a sonic difference between different converters.
Just like different amps and power cords.
The Walmart converter might sound great, thats a broad stroke to say there's no difference in the sonic signature.