In theory, dein/e can indeed be used in the suggested context.
In practice, this valediction seems to have largely fallen out of use at least among the younger generations. I exchange plenty of (electronic, but following the same form for written content as physical) letters, and I think I have never seen the valediction dein/e in that context, while (viele/liebe/herzliche) Grüße, bis bald, and plenty others are commonly used.
There is indeed one class of letters that routinely uses Ihr/e. Those are usually advertisements whose (alleged) senders try to force a sense of familiarity onto the recipient. Still, they are not trying to insinuate a romantic relationship.