Are the words vicar and vice cognates?
vicar: from Latin vicarius (i.e., someone delegated)
vice: from Latin vitium (fault, defect)
Both passed through French on their way into English.
Oh, I meant vice as in vice president (not a corrupt president 
) as in a stand in president compared with vicar, stand-in.
Oops. 
According to my dictionary, Vice \Vi"ce, prep. [L., abl. of vicis change, turn. See Vicarious.]
So, yes.