I would not trust someone who I just woke up at 2am to do something. He/she is mid-sleep. They will be prone to errors, they will be super tired, and I just ruined their next 1.5 days that it will take them to recover from that.
This is not a job where you live boxes where intellect is not needed as much, (strength and stamina will also be affected by a mid-night alarm). You want your folks to be 100% on par, otherwise they may make things worse.