The answer to your question is both yes and no. Your commander cannot make a blanket policy that says all communication must be in English during the duty day. However, your commander can force you to use English to communicate as a part of military functions. AR 600-20 para 4-13 states the following with regard to Army language policy:
English is the operational language of the Army. Soldiers must maintain sufficient proficiency in English to perform their military duties. Their operational communications must be understood by everyone who has an official need to know their content, and, therefore, must normally be in English. However, commanders may not require Soldiers to use English unless such use is clearly necessary and proper for the performance of military functions. Accordingly, commanders may not require the use of English for personal communications that are unrelated to military functions.