Not much buddleia blossom left now, the Peacocks, Red Admiral's and Tortoiseshell are making the most of it.
From what you say, I can leave the batteries in the camera and they will safely charge while the regulator is plugged in.
With the camera turned off the output is 4.8V maximum and less with camera on.
Yes, from my understanding of your setup, you should be able to get away with that. One of two things will happen. If the regulator maintains a voltage that is outside of the battery charge voltage range (i.e. the voltage on load when you turn on the camera drops, but not below 4.2V), the built in
DW01 Plus protection circuit in the battery will simply disconnect the battery (and it wont charge), if however there is a suitable voltage across the battery (see page 5 of the DW01 plus datasheet for the exact range, or assume between 2.5V and 4.25V), and the battery is not fully charged, then it will charge, with the DW01 plus protection chip keeping everything within safe limits, and disconnecting again once the battery voltage exceeds 4.2V
I would add one caveat, namely that there is no check for over temperature, which seems to be the only additional thing that the genuine canon battery and charger does check for. Having said that, all of the clone batteries have a fake thermistor in them, and all of the fake chargers lack the third pin that monitors the battery temperature anyway, so if you can live without this minor safety feature, you should be fine.
In other words, you do this entirely at your own relatively minor risk, and the above only applies to the setup you describe, and assumes the battery has a suitable inbuilt protection IC.
If you are feeling particularly paranoid, there is always the old dinner plate to fall back on for added protection.