Classic capture. Would the government's decisions be biased by knowing that the financial decisions it makes will directly affect its old (and future) colleagues? The bureaucracy can buy product A from a random company, or product B from their old boss's company. And also have some assurance that in the future, the second company would offer them a job. All the while, product A is the better product.
This is not nearly to the level of 'constitutional protections' - but is instead another indication of the inability to properly regulate an entirely secret bureaucracy. The NSA has all the failings and issues that any other large bureaucracy has - however it has difficulty utilizing the common mechanisms to regulate its less efficient behaviors.
Will there be a scramble for other highly ranked NSA employees by other companies in the same line of work?
So I'm viewing this from the implications of the effect on the market rather than the effect on NSA.