Can timestamp be used in synchronization of processes having Race Condition?
The short answer is yes, since what you're essentially doing with the timestamps is making all potentially conflicting processes sequential. Of course, in sequential systems there are no race conditions (a bit of a simplification, but nevertheless). In what way does timestamping processes differ from creating locks on resources, which is the current standard in parallel computation? You may want to reflect on what the real issues with race conditions are. Maybe this definition from Wikipedia might help: 


  "A race condition or race hazard is the condition of an electronics, software, or other system where the system's substantive behavior is dependent on the sequence or timing of other uncontrollable events."


So the primary issue to consider is what happens when you don't have control over the process(es) that cause(s) the race condition.