Well, unless it's changed, and I certainly haven't tried, it's unfortunately not possible to join a game midgame, without loading a saved game. If that's done, the new player is most likely to be taking over an AI's position (though obviously not necissarily so), and would already have all the stuff the AI had gained prior.
Though it would be nice if the ability to join a game already in progress were added. Or especially rejoin a game should you accidently fall off.
Although, that doesn't mean it's a bad idea, either way. It really would be nice to just be able to hand over ships, planets, and whatnot to another player if so desired. Assuming, perhaps in the case of ships, that they have the fleet capacity to accept them (just to prevent someone from gaining a fleet without the cap at someone else's expense). Could maybe even have missions related to that sort of thing too.