A cellular communications system may include a plurality of mobile cellular communications devices each associated with a respective user, and at least one cellular base station for wirelessly communicating with the mobile cellular communications devices. The at least one cellular base station may have a capacity associated therewith. The system may also include a central station for determining available capacity of the at least one cellular base station based upon active wireless communications with the mobile cellular communications devices. Moreover, the system may also include a subscription server for cooperating with the central station to provide non-real time subscription data to users on respective mobile cellular communications devices via the at least one cellular base station when the determined available capacity thereof is greater than a threshold.