I think there may in the future be opportunities for non tyre rated, but only when they can't get anybody TR. At the moment there seems to be plenty of 330 rated folk coming home from the gulf, the 747 I'm not so sure about.
But even when it's non type rated it will more than likely be 320/737-757 rated so they can do a shortened TR course. I think, and only my personal opinion , but it is very unlikely there will be recruitment from those rated on something less transferable ie, bae146, rj85, emb145-175-195, Q400, other turboprops and the like.
All supposition but I don't think it's far off the mark.