I'm not sure about SpaceX specifically, but if you were a Green Card holder. e.g O-1 Exceptional Ability, then you'd be considered a US Person for ITAR compliance.

From http://www.spacex.com/careers.php "To conform to U.S. Government space technology export regulations, applicant must be a U.S. citizen, lawful permanent resident of the U.S., protected individual as defined by 8 U.S.C. 1324b(a)(3), or eligible to obtain the required authorizations from the U.S. Department of State."

It doesn't sound like SpaceX require a Secret/Top Secret clearance for most of their employees. Some other space companies (Orbital Science Corp, ULA/Boeing/Lockheed Martin) do because they work on missile systems like ICBMs in related programs.

From what I understood, most engineers who make the grade to work at SpaceX, would be O-1 visa eligible as well. The O-1 is not tied to continued employment at a particular company.