There are three concerns:
1. You must have a dual-mode TV... one that supports not only the PAL standard that the UK uses but also the NTSC standard used in the US.
2. The power outlets in the UK won't support the US Gamecube's AC adaptor. You can either get some sort of adaptor to use US appliances in the UK, or if it's cheaper you can probably just buy a replacement Gamecube AC adaptor for a UK gamecube and use it with the US Gamecube.
3. Gamecubes will only run software of the region they were originally sold in, so you won't be able to buy Gamecube games in the UK and run them on an American Gamecube. Technically there are ways around this, but considering how much cheaper GC games are in the US than in Europe, I'd just have him make sure to buy all the games and bring them with him.
If you have specific questions, there are video game import shops that will likely be able to help you out.