Do whistleblowers have right of privacy on password-protected emails from work?

Does a government agency have the right to monitor employees’ personal email accounts if those accounts are accessed on a work computer?
That the question being raised in a recent lawsuit brought by six scientists who had reported alleged irregularities in the Food and Drug Administration’s medical device review process.
The staffers alleged that “the FDA scientists noted that in the past, computer-aided detection devices (‘CAD’) to be used with breast mammograms were not safe or effective, but the FDA approved the devices anyway in a flawed process that ignored the science.”
The whistleblowers claim the agency launched “a covert and secret search and seizure operation” in retaliation for their speaking up.
FDA officials pried into private, third-party, non-Governmental, password protected and encrypted email accounts on Google and Yahoo, the whistleblowers allege, using the information gathered to retaliate against them.
A First Amendment issue?
Jaikumar Vijayan, writing on computerworld.com, quoted Hanni Fakhoury, staff attorney for the Electronic Frontier Foundation, who said the case presents some “really interesting questions about the right to use your email at your workplace.”
Adding to the complexity of the case, Fakhoury said, is the fact that whistleblowers were at the center of the dispute:  “That may be a whole separate legal issue under First Amendment law,” he said.
We’ll keep you posted. To read a redacted version of the whistleblowers’ full complaint, go here.