No a form can't make use of mod_rewrite - but that's not the real question in your mind.
What you meant to ask was a means to reformat the link displayed when submitting the form.
What I would do is simply use method="POST" rather than your method="GET". That would conceal the query string you're concerned with.
What you're really asking is whether you can use mod_rewrite to make a "loopy redirection." That answer is yes but I'll merely refer you to the tutorial linked in my signature as there are a couple of ways to do this in the sample code section. If you're not making use of reference material posted here, answering these questions constitutes "spoon feeding." Read then ask questions, if you please.