No, we'd write it the first way, even if the quotation ended with punctuation not appropriate to the sentence as a whole: e.g.
> Bill asked "Do you prefer American style?"
even though the sentence, taken as a whole, is a statement rather than a question.
I'm thinking of a sentence like:
> Bill said "I prefer American style."
Would the British write it as follows?
> Bill said "I prefer American style.".