Yes that's exactly what I'd expect to see.

    He said "I came in with the tide.", but she wasn't listening.

(which is correct according to my expensive British education) is very preferable to

    He said "I came in with the tide.," but she wasn't listening.

which has a full stop and comma next to each other and looks hideous.

However, I do personally think the full stop inside the quotes is redundant and would remove it, unless it made a real difference to the sentence meaning.