D.C. v. Heller
Umm...stupid question but...did Heller change anything?
I mean yeah, you'd have to go to court but...this IS the Federal government we're talking about...the group specifically bound (so far, until we get incorporation) by the "personal defense is a basic civil right" part of Heller...
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No worries friend, there is no such thing as a stupid question.
Heller clarified meaning of the the 2nd Amendment to include an individual right to possess a firearm for private use.
Individual rights and your rights as a government employee using government property are two totally different things. Because the gov't owns the rig, and you are their employee, the gov't has broad discretion to proscribe certain activities and behaior. (E.g., smoking, carrying a firearm, etc...)
For example, think of 1st amendment free speech protections. Political speech made by private citizens receives a high degree Constitutional protection under the 1st Amendment. Yet the gov't may proscribe political speech in the gov't workplace, or even speech concerning internal office affairs. See e.g. Connick v. Myers, 461 U.S. 138 (1983).
So to answer your question - no. Heller does not affect this issue.
HTH