By beforehand, I mean before Farengar gives you the quest to? I just started a character that went straight to Whiterun and received the quest to get the Dragon Stone. This is the FIRST time I've done it this way. When I returned, much to my surprise...
Spoiler
Delphine was there in her adventuring getup talking to Farengar!
85% of the time I tend to go in AFTER the quest, from a more "realistic" stand point, why would you even want to go in there in the first place, espeically if you heard rumors that the place is haunted.
I must say though, what happened to you in the spoiler, I don't recall ever happening to me yet, hope it does next time I get to it!
On my first playthrough, I went straight to Bleak Falls Burrow for the dragon claw. Had no idea about the Dragonstone, although I stumbled upon the draugr who was carrying it, on the way out
On the later runs, I'd pick up the dragon claw quest, but head to Whiterun instead. Yes, I know about the scene you described