No they don't, although the XBLA trial versions do appear in my download list on 360, having downloaded them years ago.
Just Banjo Kazooie and Banjo Tooie
Nope, not shared. In fact the console was factory reset recently as part of the NXOE stuff and since then only my profile has ever signed in. They're still in the list.
So overall there's no reason I should be able to play the full versions of these. But they've been there since day 1 of the BC preview. I've since bought Rare Replay digitally, so now there's 2 versions of both games in the install list.