Yes, you can go to jail / prison for flying under the influence.
This isn’t just an FAA thing saying you can not fly anymore. The FAA is a safety / regulatory environment with the US Attorney to reck your world if they decide you acted with criminal intent to violate the regulations…
You can go to federal prison after you do your state time. Most people don’t know this. One is a federal crime, one is a state crime. No double jeopardy, only double the time.