He absolutely did not, he went out of his way to avoid bringing religion into the race as he thought it'd actually play into Kennedy's hand.

Other than hating Kennedy for a set of reasons that had nothing to do with Kennedy being "Catholic" Nixon believed if he or anyone on his campaign tried to pull the old papist card that it'd backfire horribly. Nixon (rightly) presumed that most Americans, especially moderate Republicans and almost all Democrats were either past the point of believing in such conspiracies or were, in Nixon's mind, warming to the idea of patting themselves on the back for NOT disqualifying Kennedy simply because of his religion.

For sources see Nixon's memoirs (RN, first volume if you're reading the paperback), I think Six Crises has quite a bit on that too, or if you're in the Anaheim/Yorba Linda area, stop by the Nixon Library,ask to go to the archives room and ask any archivist to look at the Six Crises drafts, because it's definitely in there.