No. In the FAA system the person issuing your certificate determines if you can speak and understand English. Your FAA certificate will only say you are "English Proficient" and not say anything about a particular level. The guidance for the person issuing your certificate says
"English Language Requirements. Early in the process of issuing a U.S. pilot certificate, that is on the basis of a foreign pilot license, the FAA aviation safety inspector (ASI) (Operations) or an FAA aviation safety technician (AST) must determine whether the applicant can read, speak, write, and understand the English language."
You are using your Japanese license to fill the requirement that you hold a commercial license before you get an ATP.