I'm fairly sure you need to at least be a Permanent Resident to get hired, which makes you a US Person (it's a distinct legal definition). Permanent residents are also able to join the military and have been able to do so for a long time. There's enough of them that during the peak of the Iraq War they even held in-country citizenship ceremonies at major bases for people who had filed and completed their citizenship paperwork.

US person is a tax definition, folks without permanent residency that meet the substantial presence test are also US people. For immigration purposes you use resident alien / nonresident alien.