Not exactly. True Tone function in M1 and above models is dependent on whether the LCD’s serial hash matches the hash of the Logicboard. This serial is stored on a chip that is soldered on the T-con board that comes with the inner LCD.
The reason why people say True Tone works with inner LCD replacement is only true for M1 14inch and 16inch models because Apple went a step further to disable the entire screen function if the serial does not match the xx after an LCD replacement, unless it is calibrated (paired) by their GSX technician.
To resolve this issue, the third-party industry now de-solders the chipset containing the serial from the old LCD’s T-con board to solder it on the new inner LCD. It can be done with a full LCD assembly AS WELL, but it’s seldom done as it is riskier to damage an expensive full LCD assembly.