Over the next twenty minutes, the patient's alertness slowly improves. Because of his chief concern and this seizure, the ED has decided to admit this patient. You admit them to your service.
If his mental status has actually returned to baseline, and there were no other concerns (e.g. abnormal movements that require spell capture for determination of whether or not they're seizures), then no, cEEG is not needed here.
In this case, yes, cEEG is indicated to rule out non-convulsive status epilepticus, as he hasn't yet returned to baseline, and his improvement has plateaued.
Of course, in the moment, you may not feel like waiting to find out. An alternative option would be to place a rapid-response EEG device as soon as the convulsions end and you've ensured the ABCs have been managed. If it immediately rules in status epilepticus, then treat the patient as such while waiting for the full montage with cEEG to be connected. Or, if this doesn't clearly reveal status, then you can keep it on for the full 30 minutes. After that, if the patient has recovered to baseline, then cEEG would not need to be started. If the patient hasn't yet recovered, though, then that'd be a good reason to connect to cEEG.