The feasibility of a quantum-classical hybrid network using multicore fiber is explored and key performance metrics of the quantum channel with respect to co-propagating classical light are examined. Multiple commercial time bin quantum key distribution systems from ID Quantique are characterized using direct injection techniques to determine optimal operational parameters for the classical optical channels in order to minimize the quantum bit error rate and maximize secret key generation. A phenomenological model that determines the expected quantum bit error rate for a wide range of injected input wavelengths and powers is utilized to evaluate the quantum key distribution system performance. Analysis shows that the performance limitations exhibited by the tested commercial quantum key distribution systems in a hybrid network based on multicore fiber could be overcome by a strategic choice of the classical channel parameters.