It's not aware. The information that it had been interrupted would be something we can easily add to the next user chat request. Where exactly is harder, because at least for Coqui XTTSv2 we don't have TTS wordstamps (we do have them for Kokoro though).
So adding the information where it had been interrupted would be easily possible when using Kokoro as TTS system. With Coqui we'd need to add another transcription on the tts output including word timestamps. That would cost more compute than a normal transcription and word timestamps aren't perfectly accurate. Yet directly after an interruption there's not that much concurrent need for compute (like in the end of turn detection phase where a lot of stuff is happening). So I guess with a bit of programming work this could be integrated.