Would this still happen if Doc has ADSB transmissions?
I am afraid so, Mode-A, Mode-C, Mode-S/ES are independant of each other.
When the transponder responds to a Mode-C interrogation, it simply sends a 24 bit response which is interpreted
as 4 octal values between 0000 and 7777
There is no way to correlate this information with ANYTHING else the transponder has produced.
All 1090Mhz transmissions were invented in the dark ages, using a modulation technique (Pulse Position Modulation) that is never used in any modern system. When the US introduced UAT on 978Mhz which runs complementary to 1090 transponders, they chose to use FSK (Frequency Shift Keying) as a superior modulation technology.