It did, but the duration of the stay is all hypothetical. There may be some folk tradition that speculates on that, but no doctrine. We don't know, for example, how long it takes to purge the aftereffects of a murder, or a broken fast. I would venture to say, we know that it is not knowable. This is one of those things that were a problem with indulgences.
I see what you are saying. It is an area of speculative theology. The punishment is God's choice. We can't know except through revelation.
The Holy Father did recieve Anointing of the Sick, viaticum, and absolution before he died. Somehow I don't think he'll spend too much time in Purgatory, if any at all. I venture that he is in Mary's arms (or will be very soon).
Now we pray for him. Soon I will ask him to pray for us.