Of course. If you promise to do something, but don’t intend to follow through, did you still make that promise? Yes you did. If that promise was legally binding (as in an oath of office or oath before a court) you can of course be held accountable for that oath whether you “believe” in the thing or not. Can you imagine what a mess it would be if you could just say “well I don’t believe in the Bible, so I can lie in front of a judge all I want since they made me swear on a Bible”?
Of course. If you promise to do something, but don’t intend to follow through, did you still make that promise? Yes you did. If that promise was legally binding (as in an oath of office or oath before a court) you can of course be held accountable for that oath whether you “believe” in the thing or not. Can you imagine what a mess it would be if you could just say “well I don’t believe in the Bible, so I can lie in front of a judge all I want since they made me swear on a Bible”?