this IS interesting...because of Hilary's involvement with the Health care Task Force in 1994, whether or not she was actually a federal employee or not, wound up being litigated-and as I recall, it was determined that in her capacity as first lady, she was indeed a federal emplyee. As to whether or not this implies presidential appointment per se, I'll leave to Clintonian parsing-but I am sure it does.
Once again, whether or not Hillary served Bill Clinton in some official function has no bearing as to whether she would have been eligible to succeed him. Here is the relevant section from the 22nd Amendment:
and the Congress may by law provide for the case wherein neither a President elect nor a Vice President elect shall have qualified, declaring who shall then act as President, or the manner in which one who is to act shall be selected, and such person shall act accordingly until a President or Vice President shall have qualified.
And here is the succession for president, as passed by Congress and signed into law by Truman in 1947:
The cabinet members are ordered in the line of succession according to the date their offices were established.
The Vice President Richard Cheney
Speaker of the House John Dennis Hastert
President pro tempore of the Senate1 Ted Stevens
Secretary of State Colin Powell
Secretary of the Treasury John Snow
Secretary of Defense Donald H. Rumsfeld
Attorney General John Ashcroft
Secretary of the Interior Gale A. Norton
Secretary of Agriculture Ann M. Veneman
Secretary of Commerce Donald Evans
Secretary of Labor Elaine Chao
Secretary of Health and Human Services Tommy G. Thompson
Secretary of Housing and Urban Development Alphonso Jackson
Secretary of Transportation Norman Yoshio Mineta
Secretary of Energy Spencer Abraham
Secretary of Education Roderick Paige
Secretary of Veterans Affairs Anthony J. Principi
Secretary of Homeland Security2 Tom Ridge
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So there is no Constitutional prohibition of someone serving under a president from succeeding him.