Yes, you can use localized Japanese versions of software without a localized operating system, but only if you have the Japanese Language Kit installed. It provides the ability to input Japanese text into localized or WorldScript-aware applications.
The Japanese Language Kit is basically installed on top of an existing System 7.1 system. If the existing system is the U.S. version of System 7.1, then the primary script (what language the system boots from and displays -- for instance, the menu bar) is English. But you can now launch Japanese versions of applications and input Japanese characters just as if they were running on a localized system.
You can also use WorldScript-aware applications with the Japanese fonts, if they have the Japanese Language Kit installed.
You can find a list of current localized Japanese and Worldscript-aware software in the Tech Info Library under "Japanese
Language Kit: Overview". The article includes the compatibility list.