This theory is actually vastly belived in the discord server, but it obv never got a confirm by the authors.
The only problem i see is the fact you do in fact find the Key even in rune's route, Wich can mean only two things: either Mikko found a way to put it back there overnight or before arvo got in the room or mikko didn't actually took the key.
Another moment where he could have put the Key in the bag could be after Mikko plays the piano, but the bag won't be left alone if you refuse to play too, so that would make little sense.
The only certain things is this is kinda suspicious