Yep, definitely! Think about trying to put out a big fire with a kink in the firehose, or doing it with a garden hose instead of one with a 2" diameter- - - - - -there's just not enough volume to get the job done. Your generator was trying to meet the demands of the electrical system, ignition, lights, radio, etc., and still have some current left over to recharge the battery. Those few remaining strands of wire were like the kink in the hose- - - - -restricting the flow!
Jerry