I don't expect him to be fired during the season.
Does anyone think the Mannings would be okay with Arch coming here under the current regime? I don't think they would want him anywhere near this dumpster fire.
If Allen is still the coach at that time, sure, but a new coach and new outlook would be interesting.
That said, both Peyton and Eli went to the teams that drafted them, so Arch will probably go wherever he's drafted. If the Saints happen to need a QB and can draft him where he should be, then I don't see anything preventing that from happening.