I was just looking it up on Wikipedia and it says on there that if you are not a British or Commonwealth citizen, you can only be made an 'honorary member' and cannot be addressed as Sir or Dame. However, if you later acquire Commonwealth citizenship, you can be made a full member.
So, that implies to me that if she still holds her UK citizenship and is a dual citizen (according to her Wiki page, she retained her UK citizenship when she naturalised), then it's not a problem and she can accept the honour, regardless of her US citizenship.
I also believe it says that if you lose your British citizenship, then you are still considered to be a full member as long as you were a British citizen when you received the honour.