No. You cannot directly download US PlayStation Store games on a Japanese PS3.
Why
Account region lock: PSN account region is fixed at creation. A JP account accesses only JP Store.
Game region lock: Most PS3 games are region-locked (BLUS vs BLJS IDs). US DLC won't install on JP disc/game.
Firmware differences: Regional firmware variations can cause issues.
Workarounds (Caveats Apply)
Create a US PSN account on the same PS3 → switch users → access US Store → buy/download. But: You need a US payment method (US PSN card, PayPal US). DLC must match game region (US disc or US digital game).
Import physical US disc: May work if game is region-free (check PS3 region list). DLC still needs US account.