If silence could be recorded completely, would playback include the things people chose not to say?

A complete recording of silence would still miss the largest part of it, because what makes a silence particular is what was withheld inside it. The audio would be identical for a comfortable pause and a refusal, and the meaning lives entirely in the unspoken content. Silence is made of decisions.

So pay attention to the shape of the quiet in your conversations. Was that pause peaceful, or was somebody deciding not to say something. You are allowed to ask, gently, whether there is something they nearly said. It is one of the more useful questions available and it is rarely asked.