I see my batteries settling down to between 1.32 and 1.38 V after I have removed them from charging 24 hours previous. I would regard that as the volt level on a fully charged cell.
So if you leave the charger connected 24/7, then regulate its volt level to 1.35 V times the number of cells in your battery pack. Plus or minus a few hundredths of a volt.
If it is greater, then it will subject the cells to a few mA continual charge. A little is okay, but more will be bad for them, depending. You should investigate the safe limits for your batteries to make sure.
If it is less then the batteries may be slightly undercharged. This won't hurt them, but they will provide power for less time.
As for the supply's current capability, you must decide whether it needs to be sufficient to (a) power the device by itself, or (b) power the device AND charge a low battery pack.