It does on Bosch since about 2013 I think, 2020 motors are harder again to get around if at all possible. The log they talk about is more to do with motor load vs cadence vs wheel speed, it kinda works out that something has changed when the kwh per certain distance has changed. Bosch know if the motor is changed when interrogated by a main dealer/warranty interface. This is all just from what I've heard from other shops, I don't have a bosch account.
Shimano, less of an isssue, there is a battery log, which does sort of the same thing but AFAIK its a log kept in the battery, not the motor. If you use one of those wheel speed sensor 0.5x jobs, then it'll likely be obvious when the motor/battery has seen a lot of duty, yet the odometer says half the distance vs. anticipated wear.