Does ATC use mode S addresses to identify planes?
The Mode S address is not used for identification of aircraft in the higher levels of the ATC system such as the Flight Data Processing System. 

Mostly the assigned 12 bit code (also known as Mode A code or squawk code) is used to correlate a radar track to a flight plan. The major exception is that in Europe, when the Mode A code is set to 1000 (octal notation), the Mode-S downlinked Aircraft Identity (ACID) is used for flight plan correlation. This is to free up Mode A codes. Usually planned flights are assigned discrete Mode A codes but using ACID / Flight ID correlation, multiple aircraft on a flight plan in the same area can use Mode A code 1000. 

The downlinked ACID must be equal to the Flight ID used to file the flight plan. 

The Mode S 24 bit address is only used in low level systems; in the Mode S radar, in multilateration systems, in ADS-B receivers and to some extend in tracking systems.