No. ADS-C reports are set up by the ground. A typical FANS1/A installation can handle up to 4 ATC ADS-C requests plus one from the operators AOC (Airline Operational Control) centre.
ADS-C is kind of like a transponder. The crew have nothing to do with it except to enable the function. They can also disable ADS-C reports. They cannot alter the content of such a report.
An excellent desription of ADS-C is available at
ADS