I'm British, living in the UK, but I have a US bank account.
Originally I changed my bank address to my UK address when I moved back home, but because it's a different format to US addresses, I wasn't receiving any statements or anything in the post - half of my UK address was missed off the envelope window, so I have a year's worth of bank statements floating around USPS somewhere, undelivered!
So, I changed my bank account to my aunt's address in the US, because it was easier, and now she forwards me replacement debit cards and things. There was no problem with doing this at all.