Hey guys, I'm on my fourth playthrough of Skyrim and I have a question. I would like to knock out a chunk of the Civil War quests before I start the main storyline (looking to purchase the house in Hjerim). My question is, what will happen if I bring the Dragonstone from Bleak Fall Barrows to Whiterun AFTER I complete the Battle for Whiterun on the Stormcloaks side. Will the court wizard still be there? Will the new Jarl of Whiterun function the same as the old? Thanks for your help.

You can't complete the Battle for Whiterun until after you do Dragon Rising.

More specifically, Jarl Balgruuf will refuse to give an answer to Tullius or Ulfric until you've killed the dragon at the watchtower.