Generally this is not the case. Lead acid have an out/in efficiency of about 60%, Lithium is ~96%.
Whilst a BMS has to consume some power, this is generally insignificant compared with the total energy stored in a battery, or the self consumption of an inverter.
The major issues with some BMS is that the resistive balancing current is too low. Balancing does take some energy, and newer systems use active balancing, where 90% of the balancing energy is fed back into the system.