Powering the load while charging 3s 18650 battery with BMS balance charger PCB
(TY AG I read too fast, and thought load is on the battery rather than on the charger which is OK)
Apologies
Certainly, you can load the charger and reduce its capacity while charging the batteries at a lower CC rate.

Previous Answer to a different understanding.
If you had the load on the battery side,  you should cut charging to the battery if it is already in CV mode as the load will prevent cut-off @ 5% to 10% of CC.
This requires that you have a separate current sense for the battery rather than from the charger to both batteries and load.
Laptops sense battery current separately from the MOBO and so do mobiles from external chargers.