For many, this is no longer a valid question and the case is considered settled with software defined networking/network function virtualization (SDN/NFV) providing the inevitable innovation enablers toward the realization of a virtualized, programmable, and flexible 5G network. As SDN along with other technology enablers (including NFV) are still in the process of evolution, the first commercial deployment of 5G may take few years. However, some companies are claiming the availability of 5G solutions, but considering the monumental task of softwarization of mobile cellular networks there are genuine concerns that we may only see some point solutions involving SDN technology instead of a fully virtualized SDN-enabled 5G mobile network. In order to determine the technology readiness of SDN solutions in the context of 5G networks, this survey paper attempts to identify all important obstacles in the way, and looks at the state of the art of the relevant research. This survey is different from the previous surveys on SDN-based mobile networks as it focuses on the salient problems and discusses solutions proposed within and outside SDN literature. Our main focus is on fronthaul, backward compatibility, supposedly disruptive nature of SDN deployment, business cases and monetization of SDN related upgrades, latency of general purpose processors, and additional security vulnerabilities that softwarization brings along to the mobile network. We have also provided a summary of the architectural developments in SDN-based mobile network landscape, including deployment options for SDN within NFV framework, as not all work can be covered under the focused issues. This paper provides a comprehensive survey on the state of the art of SDN-based mobile networks and clearly points out the gaps in the technology.