Yes, there should be a rather large gauge wire connected to the alternator output terminal. That is why you’re charging the battery with a trickle charger, the alternator cannot charge the battery if it’s not connected.
"The alternator stud should have batttery voltage on it at all times. Be CAREFUL. That is a high current circuit and IS NOT fused except for the main fuse link, which is poor protection"
I guess I thought that answer should be obvious. YES big wire and YES dangerous if you are not careful Disconnet battery before screwing with this