If the transponder is designed to the DO (aka RTCA) and TSO specs, there should not be an issue. Mode A /C transponders are designed to limit their replies at 1200 PRF (Pulse Repetition Frequency) - at 1200 PRF the reply rate shall no more than 95%. As the replies increase, the reply rate of the transponder decreases thereby protecting the transponder from high duty cycles and reducing frequency congestion. Mode S transponders interleave the Mode A/C function within the Mode S function.
Mode S (with TCAS II) is designed for an aircraft density of 0.3 aircraft per sq nmi. The spec is: TCAS II shall provide resolution advisories in the vertical dimension (climb, descend) in airspace densities up to 0.3 aircraft per sq nmi. This equates to 24 aircraft within a 5 nmi radius of a TCAS II equipped aircraft.
On the airborn side; as stated above, Mode S / ADS-B broadcasts (squits) its information once a second. Also, TCAS sends an All Call, and then then interrogates the responding aircraft in its airspace once a second with TCAS interrogating both Mode A/C and Mode S aircraft. TCAS II also has the capability to actively track and display up to 31 aircraft with additional aircraft in "monitor" status. Each of the aircraft in track is interrogated once per sec by TCAS.
On the ground side, the ground stations will interrogate the Mode A/C transponder once every 5 seconds or 10 - 12 seconds depending on the airspace. In the terminal / approach environment the interval is up to 5 sec whereas in the en route environment it is 10 - 12 seconds. Also, if equipped, the ground stations will broadcast the TIS data on the 1030 MHz Mode S link.
A number of techniques a used in TCAS to decrease the amount of RF traffic. For example, TCAS can focus it's interrogations for a specific target in a specific direction. Also, with Change 7.1 TCAS includes Interference Limiting. As TCAS senses higher traffic density it will decrease its transmit power to decrease the range of the interrogations to those aircraft that pose the greatest threat and periodically monitors the other aircraft in the track list.
Hope this gives some sense to what occurs on the transponder frequencies.