It totally depends on how our current picture is produced, and whether or not the new Adventure Portraits are replicated in the Lodestone or not.
Right now, the Portraits are in-game only, incorporate a lot more data to transfer out of the game, and, as some people have mentioned, are not under the control of Square Enix as far as content. Adding to that, the customization possible, and the relative size of the current picture, make it unlikely that a 1-to-1 exchange would be pleasant enough when viewing it on the forums.