The Captain America comics have gotten some good mileage out of that theme over the years - what do you do when the ideals you supposedly represent no longer reflect the actual nation?
If done thoughtfully, it can be an asset, rather than a liability.
Yeah, it's definitely possible that Picardo could play both versions of the character, even if it's just for a single episode.
But the full-time version on "Academy" will be the original, not the "Living Witness" backup.