If the Hash Rate Suddenly Doubles, How Soon Will the Next Difficulty Adjustment Occur?
The difficulty adjustment will still occur after 2016 blocks have been mined, regardless of how quickly that happens. If the hash rate instantly doubles, the average block time would drop from 10 minutes to approximately 5 minutes.
This means the 2016 blocks will be mined in about 7 days (2016 blocks 5 minutes/block), causing the adjustment to happen in half the expected two-week time frame.