Effect of Discontinuous Conduction Mode of a Buck Converter on Charging IC
There will be no problem when you are in DCM.

Yes your inductor current will go to zero for a certain amount of time each switching cycle. But this doesn't mean there is zero current flowing between the buck converter and the battery charger! Instead, the current is flowing from the buck converter's output capacitor during this time. The buck converter is monitoring the capacitor's voltage (which is just the buck's output voltage) and once it falls below a certain threshold, the buck converter will start another switching cycle.

Comment if anything is unclear!