I don't think the Saints will change Hill being designated as a QB. The main reason may have to do with the possibility of losing Carr to an injury that forces him to miss part or all of the remaining season. The team may elect to play one or both of the younger QBs, but there's the possibility of Hill playing a lot more snaps at the QB position in that situation.
The recognition and accolades shouldn't be based just on the players designated position, but rather it should be based on the plays/snaps from a given position and the results thereof. An example of that could be that a Tight End could also be the teams long snapper and could be the best long snapper in the league in a given year. The same could be said if a position player was also the teams punter. If you put up the best numbers from a give position in a season you should be recognized for doing such, not denied because of a position designation, IMO.