Sample size of one. Bay back when I had an offer from a three-letter agency, I wouldn't have been pseudonymous but I would have been officially working for some other government organization. I also had to book my own travel and they paid my expenses in cash on the spot.
That's going to depend more on what your role and assignment is than just the fact that you work for the NSA. In general though, working for the NSA isn't an anonymous act.
Good question! I'd love to know the answer to this, too.