Unfortunately, it'll be more than that, as that'll be saving the plaintext files transferred internal to the TLS connection. The information that would need to be saved will normally just be thrown out, as it'll be the TLS connection itself.

On second thought, though, I don't think that it'd be viable, since the way that something like this normally works is to just use (slow) public key encryption to transfer a symmetric session key and to then use (fast) symmetric encryption on the bulk data, and once you have a copy of the session key, you could forge whatever you want with it. This would only work if you were using asymmetric encryption to encrypt the data in the connection.

kagis

https://www.cloudflare.com/learning/ssl/what-is-a-session-key/

What is a session key? Session keys and TLS handshakes

The TLS (historically known as "SSL") protocol uses both asymmetric/public key and symmetric cryptography, and new keys for symmetric encryption have to be generated for each communication session. Such keys are called "session keys."

Yeah. Oh, well. It was a happy thought for a moment.