No it is not.
A lithium battery that is drained below 0% (overdischarged) have a good chance to get damaged.
0% SOC (the battery manufacturers 0%, not the Tesla on screen SOC) is defined as the discharge voltage limit. This is not a completely empty battery. For NCA cells this is 2.5V / cell.
This discharge level is completely safe, and the battery will have the lowest calendar aging / degradation at this SOC level.
View attachment 845069
It is very clear that 0% SOC is not only completely safe, its avtually the best SOC to have a lithium battery at.
The research is not unsure at all on this point.
Tesla use a 4.5% buffer below 0% on-screen-SOC. This means that 0% SOC on the tesla screen is about 4.5% true SOC. This is not in anyway close to a overdischarged battery. Tesla disconnects the battery via the contactors before it reaches dangerously low levels.
If low SOC was dangerous my battery would have gotten damaged, as I have been to 0% and below several times. Two times down to about -2% and to zero sereval times.
Down to 0%, last time was about one week ago when I did a degradation test. My 2021 M3P with 46.000km still has 79 kwh capacity, which means my car is among the M3P ‘21 with the lowest degradation.
According to teslafi, my car has the highest range of the M3Ps that has reach the same mileage. I often arrive with below 20%, and let it stand until next morning when the charging commence.