2,000 yen notes are actually pretty common (and popular) in Okinawa, and this is a pretty well known fact in Japan. (The art on them is a tribute to Okinawa.) So someone might be a little surprised to get one on the mainland at this point, but they'd probably just figure you'd been to Okinawa. They are well circulated there, including by banks. Consequently, they're not unheard of all over Japan.

I don't think they're quite the level of rarity as a US $2 bill. Maybe more like a US Sacagawea dollar coin, which are also very regional.