Best practice: Should I charge a battery while also pulling load?
It is very common to have a charging source, battery, and load connected in parallel so that it may look like you are charging and discharging a battery simultaneously.

What actually happens is that if the charging source can supply more current than the load demands, the excess current will go to charge the battery.

If the load demands more current than the charging source can supply, the extra current will be supplied by the battery (discharging the battery).

The battery will change between charging and discharging automagically as the load demand and charging current vary.