The external dump log will not have the status mentiond directly as online of offline.
However, if you are looking to find out whether the SEP cleint service was stopped on a computer at a particular date/time, you may search using the following syntax (full or partial)
Example1: "2015-11-10 18:18:38,Info,MachineName,Category: 0,Smc,Symantec Management Client is stopped."
Example2: 2015-11-10 18:19:30,Info,MachineName,Category: 0,Smc,Symantec Management Client has been started.
If you can find the time of the above 2 events, then you can say that the client service was stopped between these time.