Surprisingly enough, we have not had any reports of misconnects in the forum, so no actual reports of what happens. There has been reports that they are good at holding flights to avoid missed connections. But I guess actual missed connections are pretty rare. At least ANA and JAL does not suffer from the operational chaos that their US counter parts do, so cancellations are not as frequent. Unless you also count the rolling reduction of schedule. But that happens about 3 months out for the majority, not last minute.

If it is clear before departure that the connection will not be possible, I think they would stop you from flying to Narita. The terminal closes overnight, and is not geared for "staying guests"

If you make it to Narita and the connection is missed, they only have two options. Return to sender, or confine you somewhere in the terminal while it is closed. As the terminal is meant to be empty overnight, they can't have passengers roaming freely.

In that aspect a Haneda connection might be smoother, as the terminal is open 24/7.