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Using Monte Carlo simulations, we investigate how geometric percolation and electrical conductivity in suspensions of hard conducting platelets are affected by the addition of platelets and their degree of spontaneous alignment. For aspect ratios $10, 25$ and $50$, we consistently observe a monotonically decreasing percolation threshold as a function of volume fraction. In the nematic phase, the distribution of particles inside the percolating clusters becomes less spherically symmetric and the aspect ratio of the clusters increases. However, the clusters are also anisotropically shaped in the isotropic phase, although their aspect ratio remains constant as a function of volume fraction. Mapping the percolating clusters of platelets to linear resistor networks, and assigning unit conductance to all connections, we find a constant conductivity both across the isotropic-nematic transition and in the respective stable phases. This behaviour is consistent with the other observed topological properties of the networks. On the contrary, using an anisotropic conductance model, the network conductivity decreases with increasing volume fraction in the isotropic, and further diminishes at the onset of the nematic. Hence, our observations consistently suggest that unlike for rod-like fillers, the network structures that arise from platelet suspensions are neither very sensitive to the particle aspect ratio nor to alignment, thus rendering platelets less versatile fillers for dispersion in conductive composites.