The fake time can be synced to real time at the beginning of the time slice of a process. So the process never sees the real time, but the fake time is fairly close to it.
If passing data involves frequent switches between processes, then, yes, I see there would be a problem with syncing on every process switch. I think syncing at longer intervals would solve that problem. All processes could share the same fake time, but see the fake time skip a small fixed amount at fixed regular intervals. That fixed amount of fake time would take a variable amount of real time, which absorbs the small variations in real execution time.