Yes, they were brought home and yes, they were exported as Japan disarmed. The same war surplus dealers who could sell Lee Harvey Oswald his Carcano also sold surplus Mausers, Schmidt-Rubins, Moisin-Nagants, and Arisakas. And a fair number of GI's coming home from the Pacific theater grabbed them as trophies as well. You can easily spot the difference between the trophies and the exports. The trophies still have an intact Chrysanthemum imperial crest on top of the receiver ring, the exported ones have the crest ground off.

I have not checked to see if there are a lot on the market right now, but unlike Mauser and Springfield 03A3 rifles, Arisakas did not sporterize elegantly. The metal finish was often crude, the stocks as well, and though the actions are amazingly strong and the 7.7 Japanese cartridge perfectly good for large game, those other military rifles had better finish and better build quality.. If there are now more Arisakas around than the others, that could be because fewer of them have been converted into hunting rifles.