Yes they would.
After one hour passes, the ATC is not obliged to tell the pilot. The ATC can forget that there was a deactivation/reactivation (but not that the airspace is active) after the hour and, on handing over to a new shift, may not even mention the occurrence.
It is up to the pilot to receive the information himself - ask the ATC, listen to the ATIS, dial up the iPad notams.
In this case he had left C airspace 20 minutes earlier and ATC might have seen him heading towards the area but would be expecting him to know of the activation and to arrange a clearance, which he did.
Last edited by uncle8; 24th Sep 2014 at 06:22.