We investigate topological electronic responses in a kagome altermagnetic metal hosting a compensated coplanar 120^∘ magnetic texture. Using a minimal tight-binding model containing nearest-neighbor hopping, noncollinear exchange coupling, intrinsic spin–orbit coupling, and a time-reversal-odd loop-current order, we disentangle the magnetic, orbital, and relativistic mechanisms governing the electronic response. The exchange field produces pronounced momentum-dependent spin splitting and spin-polarized Fermi surfaces without generating a net magnetization. Nevertheless, in the absence of loop-current order, a hidden antiunitary symmetry TC_2z enforces vanishing Berry curvature and intrinsic anomalous Hall conductivity, even for finite spin–orbit coupling. A directed imaginary bond order breaks this protection and activates finite Berry curvature and a sizable, strongly filling-dependent Hall response already in the nonrelativistic limit. Spin–orbit coupling subsequently reconstructs the avoided crossings and redistributes the Berry curvature, enhancing or suppressing the Hall response depending on filling. For sufficiently strong loop-current order and spin–orbit coupling, a global gap opens at nₑ=3, and the Hall conductivity approaches 2e²/h, consistent with an occupied-band Chern number of magnitude two. Parameter-space and filling-dependent calculations further demonstrate that the Hall-active regime extends over broad ranges of exchange coupling, spin–orbit coupling, and chemical potential and remains robust against symmetry-preserving longer-range hopping. These results identify orbital-current order as an independent route for converting a Hall-silent kagome altermagnet into an anomalous Hall metal or a gapped topological phase without net magnetization, noncoplanar spin order, or scalar spin chirality.