Unlikely as the logs are appended to by CAs when they issue certificates.

Browsers could in theory contribute data but the infrastructure to support that would likely to be orders of magnitude bigger. I'm scared even thinking about going down that rabbit hole due to the expectation of what would be found (MITM evidence). :_(

I thought browsers did contribute. Otherwise any CA could issue as many certificates as they like and simply not report them. Is that really possible?

> I run my own self-signed Certificate Authority (CA) and my reverse proxy uses certs signed by this CA

There's no need to track certificates from private CAs. In order for your browser to trust the certificates you need to manually trust the CA (or your system admin will configure it). Everyone else will see it as invalid.