TT21 operation with no ICAO address

On Dec 9, 6:58*am, Andy wrote:
I'm moving this to a new thread since it has nothing to do with the
requirement for altimeter TSO.

I asked what happened if a mode S transponder was installed without an
ICAO address. *That was a sort of tongue in cheek reaction to the idea
that someone would not want their tail number broadcast to the Feds.

Darryl responded:

A Mode S transponder absolutely has to transmit the aircraft ICAO
address, a correctly configured ICAO address is required for the
transponder to actually work--bad things might happen if two aircraft
had the same default ICAO address were being interrogated at the same
time.

I like to continue that discussion.

Isn't it true that a mode S capable transponder cannot respond to a
mode S interrogation if it has no valid ICAO address?

Isn't it also true that a mode S transponder is also required to
respond to both mode A and mode C interrogations.

If both are true then doesn't it follow that a mode S transponder such
as the Trig TT21, if installed with no ICAO address, will not respond
to mode S interrogations but will respond to all mode A and mode C
interrogations.

If that is indeed the case then any new transponder purchaser who
wanted mode S capability in the future, but was paranoid about
broadcasting the tail number, could disable mode S responses by
leaving the ICAO address entry blank and use it just like a mode C
transponder.

Andy

Not to derail your discussion, but why does the notion of
"broadcasting your tail number to the feds" keep coming up? It seems
to indicate either paranoia or illegal activity. Is there some other
reason to be concerned about that?