I’ve experimented with Wordpress plugins that enable you to post images in tweets that link back to your site (where the image is hosted). They all require a compatible (mobile) client to function though. This leads be to believe that someone savvy enough with coding could create a desktop client/WP plugin that could work - only I can’t find one.
Wouldn’t it make more sense to just enable all media to display inline, regardless of where it’s hosted? I realize Twitter might not want to make it easy to divert traffic away from its partners, but if that’s the only reason, you should consider giving some of that control (and traffic) to your users. Particularly since WP users with iphones can already easily do it.