LOL, hilarious idea. There was a BBC Doctor Who novel where K9 was revealed to be behind a wall in a corridor inside the Eighth Doctor's Tardis. he had been put there by Romana, I think. This was set years after her adventures with the Fourth Doctor.
To topic, before Dirk gets us,I believe the Fourth Doctor would take it all in stride if he met his other incarnations and ne very casual and carefree about it.