Checking the night before is a helluva lot better than what many people do - which is nothing.
You do occasionally get "pop-up" NOTAMs for things like police investigations that happen suddenly - Soham springs to mind from a few years ago, for example.
You would be incredibly unlucky to get caught out by one of these, and if you were prosecuted then I would expect you could use the fact that you checked the NOTAMs the night before as mitigation.
It's worth noting that the AIS site does make it easy to do a quick update on a NOTAM check. Simply find the NOTAM check that you did last night, select it and click "Update". That will exclude all the NOTAMs you've already seen, and will probably result in a message to the effect that there's nothing there - in other words, no NOTAMs have popped up overnight. You could do this before you leave the house and it would take about 2 minutes.