TPs and Avios remain if you change address but there are a couple of things to be aware of mainly related to credit cards.

First of all, if you collect Avios on a UK credit card they will not credit to your BAEC account if you change your address to a US one. They will not disappear though and will remain ready for you to have transferred to your account once you move your account back.

Also, if you have any 2-4-1 vouchers issued against a UK credit card you will not be able to redeem them if you change your address to the US.

You can switch addresses no more than once in each six month period.

I've wrestled with this issue quite a bit over the last couple of years so let me know if you have any other questions/concerns and I'd be happy to help.