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Abstract: Axion dark matter searches require highly sensitive detection schemes with high scan rate to efficiently explore the parameter space. Building upon the conventional Sikivie haloscope, where axions convert into microwave photons inside a magnetic-field-immersed resonant cavity, we present a photon-counting scheme based on an electro-optic microwave-to-optical transducer. Through a comprehensive theoretical model under realistic experimental constraints, we find that the optimal operating regime employs an overcoupled microwave cavity, trading peak transduction efficiency for reduced transducer noise. Furthermore, combining parameters already demonstrated in existing devices, in a device with optimized extrinsic coupling rates, would yield a scan-rate enhancement of 5-10 relative to quantum-limited homodyne detection. Improvements in quality factors, coupling rates, and thermal management push this enhancement beyond 50. While our quantitative model is benchmarked at 9 GHz, the scheme adapts well to haloscopes across the 5-12 GHz range, where shrinking cavity volumes severely degrade the achievable scan rate. These results demonstrate the potential of electro-optical photon detection as a high-speed detection technique for axion dark matter searches.