No. Current is not "pushed in" to the servo or something. A servo will just use 100mA (but I think it will be more then 100mA) of the 16A. It would be a bit weird if that wasn't the case. Your house is connected to power plants that supply 1000's of amps but you're just able to plug in a 3W bulb just fine
By the way, 16A is a large supply when you don't know basic electronics...