Pyrodex contains charcoal, sulfur, and potassium nitrate (KNO3) as in real black powder, plus potassium perchlorate (KClO4). I gather the perchlorate increases the oxidation process to the point that most of the fouling is burnt up or blown out and they can advertise that you do not need to clean between shots.
None of these things are corrosive when DRY.
Charcoal is very inert and elemental sulfur is not very reactive, either.
But the KNO3 and KClO4 are hygroscopic and will absorb moisture from humid air. Each such material has a Critical Relative Humidity at which they will absorb enough to cause trouble. It is usually pretty low, and the CRH of a mixture is usually lower than the ingredients'. So unless you live in the desert, there is potential for rust. Does the patched or saboted bullet seal it off enough to protect from humidity? Apparently so, at least in some cases.
When the gun goes off, the rules change. Some of the combustion products are gases. Charcoal burnt to CO and CO2 and nitrogen released from nitrates as they oxidize the fuel are inert and long gone. The sulfur is mostly burnt to sulfur dioxide, SO2 with a little reacted into potassium sulfide, K2S. If there were any moisture around at the time, the SO2 could be absorbed to form sulfurous acid, H2SO3 which is much less corrosive than sulfuric acid, H2SO4. A small amount of sulfur trioxide, SO3 might form which would produce H2SO4 if there were any water in the 2000 degree environment. But there isn't, so what is not discharged in gaseous form to give the distinctive black powder smell reacts with the large amount of potassium present to form potassium sulfite and sulfate, K2SO3 and K2SO4. These are hygroscopic salts, but there is not going to be a lot left there.
Most of the potassium goes to form potassium carbonate, K2CO3 which is a bit alkaline. So any of those hypothetical acids would be neutralized on the spot. Carbonates are not very corrosive even when damp, either.
Adding KClO4 in Pyrodex changes the rules again. It burns to a residue of potassium chloride, KCl; just like what you get from a chlorate/corrosive primer. I have read reports of nasty rust from neglected Pyrodex guns when the humidity is up and am surprised there are not more. One early report described a concreted hard fouling in a gun left a week after shooting Pyrodex, even though it did not rust in a dry climate.
Of course this is all theoretical and small changes in conditions can have large effects in the field. The safe thing to do is to clean early and not leave your gun loaded. I wonder if the old tompion muzzle plug would preserve a loaded gun between hunts.
It sure would be nice if some enterprising gunzine writer would run some real tests on this sort of thing instead of just rewriting press releases on the latest product from his rag's advertisers.