Janeway had sex once in Seven years by herself aided by a holographic muppet.
She either didn't need sex or didn't like sex or was pissed at Mark.
Judging her by her actions alone...
Kathryn Janeway is a surgically altered Vulcan sleeper agent spy waiting for the balloon to go up.
Considering the shit Tuvok got away with and shit Tuvok let Janeway get away with, it's far more likely that he is her handler than that he is her friend who respects who entirely no matter her mad choices.