It's complicated. Shooting more hinds certainly will not hurt - but it also may not help. There are density-dependent fecundity effects where releasing acute feed competition may increase the breeding rate in the population (e.g. more first year hinds breed that otherwise would not have) - resulting in no population reduction. Shooting stags under the guise of "population control" can fall into this category - making the problem worse rather than helping.
Hunters shooting every hind seen in a certain area may result in a reduction in the population however it would be self-limiting - at a certain population level and with behavioural adaptation, even if enough effort was applied to become additive mortality (rather than compensatory as above), the encounter rate of hunters with hinds would drop off - you'd never entirely remove deer, only reduce to a certain density. Which may or may not be enough to achieve a change in outcomes, depending on your defined objective. It would be interesting to see it applied and studied.
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