Should be fine
We had the same concerns. If they accepted and processed your app, you should be fine. It means your app was complete.
We panicked after reading horror stories about the company that previously held the contract for processing visas to India and decided to do an expedited walk in, SFO CKGS.
We had our passports back with visa within a week. Barring a major holiday, I think the consulate acts pretty quickly, once it is in their hands.