If I remember correctly I think this was made after he’d been cast as the Doctor but before his episodes started airing, which means it pretty much had to be an intentional joke to cast him this way.

Spoilers!

(Which is what they say on the show when someone reveals the future, I’m not accusing you of anything.)

I just learned that he was the “W.H.O. Doctor” before becoming “Doctor WHO”, while listening to the No Such Thing As A Fish podcast within the last few days!