I'm not sure if the event itself entering into conserve mode would show up in "diag debug crashlog read". But I would expect the cause and/or some artifacts related to it should show up in it. That's why TAC always asks it when we report a problem like that.
But system event log should show an even with "conserve mode" when it occurs. If you're doing only memory logging you can't see it after a reboot. If the FGT doesn't have an HD, I recommend you send at least system event log to FortiCloud/FortiGateCloud. So that you can look them up later when the FGT was already rebooted and you get a report.