If you don't have an Amex card, then the only other issue is Tesco Clubcard - you won't be able to convert your Clubcard vouchers into BA miles while you have a European address (because your BA and Tesco addresses must match).

You will also be targeted for European offers, rather than UK offers.

But many people do EuroCheat, so there's no real reason not to if you're not worried about Amex or Tesco.

You do of course need to have a valid European address, as BA will send your new card to that address.