Being in this field, I can say that it depends on the setup. If it is directly connected to the electrical system of the car while it is inverting the power, this could void the warranty for the entire battery monitoring system and thus the car itself. Lithium batteries are controlled and monitored for safety and messing with this circuit by utilizing the LA battery as an external power supply could cause damage to the system that could result in catastrophic outcomes.
That LA battery is there for a reason. I don’t work with Tesla, but I would assume it is there as a backup for the monitoring and safety systems. There is a reason they are using an LA battery in a lithium powered car.