Your FAA license never expires. Your minimum currency to act as PIC in any kind of operation involves a current medical and current flight review under 61.56. Instrument PIC currency and passenger-carrying PIC currency are covered by 61.57. There are additional requirements if you're also talking about currency for Part 135 or 121 ops.

There are definitely others here far more qualified than me to address the practical aspects of the effect on potential employers but, FWIW, unless an application says that you need to have a current FAA Flight Review, or medical, or meet some or all other FAA currency requirements, I doubt that doing a FR in a 172 and hopping into a 172 or some other light single or twin to do three hops around the pattern will add anything to the 3-year ATR experience you have.

I'm trying to picture the discussion:

"Look this guy has been actively flying an ATR-42 overseas for three years."
"Who cares? Has he been in a 172 in the US recently?"