Actually, you'll need a flight review. While FAA certificates never expire, you go non-current without a flight review in the last 24 months. (Some events can replace the FR but we'll keep it simple.) The regulations require that a FR be minimum of 1 hour ground school and 1 hour flying. While flying is flying, I'd plan on several hours reviewing airspace and procedures, getting weather and the required mins, etc. It's not a pass/fail event, just training.
That being said, the AOPA web site has info on TSA requirements and at present they say TSA does not get involved in a 61.75 "based on" certificate. Don't know about the visa issue but I'd say if TSA doesn't think it's training ICE shouldn't care.