Not our experience...
From our experience, our senators responded promptly after the interview. DS #2 received a letter from our senator within 2 weeks of the interview informing him of his nomination. He received a letter from our other senator the next week. He received a letter from our congressman a few weeks later. All have been very prompt in responding.
We are in Florida (since I guessed this may be the next question).
If you are wondering if the senators have already sent out their nomination notifications, call and ask to speak with the service academy coordinator.
Best Wishes...