Hope this helps you out.. I've done some research, and as long as you aren't here illegally, you should be ok. HOWEVER. It is up to you to determine what your status is in respect to this application.
look at page 5 of this application.
"Federal law makes it unlawful for aliens who are illegally or unlawfully in the United States to receive or possess firearms. In addition, subject to certain exceptions, aliens who are non-immigrant status are prohibited from possessing or receiving firearms in the United States. A non-immigrant alien is not subject to this prohibition if the alien (1) is in possession of a valid hunting license or
permit lawfully issued in the United States; (2) is an official representative of a foreign government who is accredited to the United States or his or her government’s mission to an international organization having its headquarters in the United States; or (3) has
received a waiver from the prohibition from the Attorney General of the United States. See 18 U.S.C. 992(y)(2) for additional exceptions. In order to determine whether applicants who are not U.S. citizens are prohibited from possessing firearms under Federal law, it is necessary to obtain answers to the following questions."
It has a series of questions that you should look at and answer. Understand that any false statements would consist of perjury! Hope this helps.