RE: What's that sensor?
It could be a pressure switch into the oil system which could be used to prevent the alternator from trying to start charging untill oil pressure is up by interrupting the rotor, field, current from an external regulator.
Disconnect one of the leads when the engine is not running and use an ohmeter across the terminals. If it is a switch there should be infinite ohms, open switch.
Unfortunately it's hard to see where it goes on the alternator. Take a really good look at the terminal on the alternator that it connects to. There may be a cast or stamped marking next to it.
Try disconnecting it before the engine is started. If the alternator doesn't work then you have your answer. If it is indeed the rotor wire disconnecting after the engine is running would be ok but it's best not to. You don't want any chance of alternator damage of disconnecting while running if it is not.