Bad Practice - Charging Lithium Batteries while powering circuit?
The BMC measures and controls the voltage and current that is provided to the battery and do so quite precisely to improve the life of the battery (depends of the quality of the BMC of course).

If you connect a circuit, while charging, some of the current the BMC would think goes to the battery will actually go to your circuit.

This might create issue the BMC charging algorithm, especially to detect the end of charge of the battery, since you are still drawing current at a voltage the battery shouldn't.

There are different lithium chemistry, and charging profile also depends on the chemistry of the battery, some has some small fluctuation that the BMC will pick up to detect the end of charge.

To answer the question, it might depends on which battery/chemistry is used and what BMC is being used. In some case it will be no problem, in some case it might fail to detect the end of charge and go in fault. 

In case of Li-ion and Li-po, it would probably not damage the battery as the end of charge is constant voltage.

A better solution would be to power your circuit from a source before the BMC, this usually can simply be done by adding a diode between the battery and the circuit, or better with an electronic switch.