Originally Posted by
JAXBA
This.
The Avios will still collect, theoretically, but they won't post to BAEC from Chase, until you switch your address back to the US. But then your Amex Avios won't post until you switch back to the UK.
Neither account will close, but the Avios will only post from one or the other of them at a time, not both.
This was my experience too and it's why the demise of the BMI Diamond Club is such a shame. With the BMI card it was possible to earn and transfer Avios in the UK to an account in the US while also using the Chase card in the US.