Maybe Power Nap will work:
http://support.apple.com/kb/ht5394
First, this feature has restrictions: it's only in Mavericks, it only works on certain models, mail is only checked if it's running when the computer is slept, mail is only checked every hour, etc. If you can live with those restrictions, you might get it to work.
Second, in addition to the restrictions on Power Nap and Mail, it's unclear to me what kind of filtering Mail.app will do under Power Nap. Will it run filters? Will it run scripts attached to filters? I don't know. It may be that Mail only retrieves email without processing it through filters, or there are limitations on what the filters can do. The way to find out is to do an experiment to determine this yourself.