No, the RealTimeScheduler and the cParsimSynchronizer (which is implicitly used when parallel support is turned on in OMNET) are mutually exclusive. Both class is an subclass of the cScheduler calls and OMNET can have only a single scheduler. You can configure either RealTimeScheduler or the cParsimSynchronizer, but you cannot configure both. If you configure parsim-synchronizaton-class then you implicitly select cParsimSynchronizer as the scheduler implementation (that's why you receive a class cast exception as the tap module assumes that it is running using the RealTimeScheduler)
The task of a scheduler class is to deliver the messages to the appropriate modules at the right time and hold off the simulation in real time if a message is not yet available). Now cParsimSynchronizer is syncing to the other MPI processes, on the other hand RealTimeScheduler would sync to external interface cards. You cannot configure both at the same time.
In theory it would be possible to write a scheduler that does both (i.e. it sync both with the other MPI processes and also with external interfaces) if you would be able to merge the two functionality.
Sadly that would not help you anyway. You are trying to speed up the execution speed of the simulation by using parallel simulation, however it is a general misconception that parallel simulation improves always the performance. In most cases, that is not the true. Marshalling/unmarshalling the messages and passing them between different processes adds a lot of overhead to the communication between the modules. On the other hand, the different simulation partitions still have to run in lock-step to avoid the violation of causality, so syncing their simulation time is again adding overhead.
You should expect speedup ONLY, if you have a kind of simulation where there are partitions of the simulation which are tightly coupled while message exchanges between partitions are relatively rare and have a considerable delay on message delivery between them. This is not typical for an internet simulation. An additional issue with parallel simulation is that you cannot use global variables, caches, static variables etc.
For the above reasons, INET was never designed to be able to run using parallel simulation (it has several global variables, caches, modules etc.).
So in short, INET itself is not usable under parallel simulation. Sadly the only way to speed up the simulation is to use a computer with faster single threaded performance...