Can a rockman battle chip gate work with an American megaman battle network 4 game

yes, if you have battle network 4 red sun or blue moon (PAL or USA version) and you have a EXE 4.5 battlechip gate you can play operation battle, there for you must have Navi Chips (only released like exe 4.5 in Japan, or you can buy them on Ebay) and battle chips.