You dont need to press a button to send the flight id, it is collected by the SSR in the Mode S Elementary Surveillance (ELS), as is the 24 bit unique address.
I would be surpised if the standard models did not support this since this is whate EUROCONTROL are after. I suspect they are probably sending the reg of the plane by default - but thats a guess, since its one of the standard installation modes. Does anyone know what the installers set for GA?
The GTX33 and 330 support the Flight ID.