Do aviation intercoms have a standardized compatibility with radio stacks?
This is a good question - the comments above answer most of it, but here are some more details:

Short answer: yes, they are pretty much standardised. Any modern GA intercom will work with any modern GA radio.

Part of the job of the intercom is to tell the radio when to transmit, and to route the correct microphone signal through to it. This is almost always done using a single wire which signals "transmit now", and a pair of wires for the microphone signal from the headset corresponding to the PTT button that was pushed.

On more advanced integrated setups, the signals might be transmitted over a digital bus, but outside of fully integrated setups like the G1000 (and even then on some models), there are always ways to connect standard aircraft radios to the intercom.