No...
hunting the males ...of which there are always an excess... reduces both competition between males and the stress on the females in breeding season, making the females more successful in rearing young. When there are too many males there is more fighting, more injuries, and of course, nearly constant pursuit and harassment of females, which limits the amount of grazing they can get in a day, and can leave them underweight.
You are thinking like a modern hunter with access to grocery stores and no competition or predation from Cave Bears and Sabertooth Tigers to name a few.
Do you think there were enough human hunters to affect the population of the great herds of game? I’d think there were so few humans that they wouldn’t have to worry about or plan for game resource management.