Hello!
https://github.com/wikimedia/labs-tools-SuchABot did this and more - it was a full fledged gerrit <-> github bridge, relaying commits from github -> gerrit and comments from github to gerrit and vice versa. I used it successfully for a while (https://github.com/wikimedia/mediawiki-extensions-UploadWizard/pull/3#issuec... and https://github.com/wikimedia/mediawiki-extensions-UploadWizard/pulls?q=is%3A... for list of pull requests merged via that) and works quite nicely.
I stopped working on it because I got a bit bored, and nobody except me seemed to be using it :P Feel free to re-use / ressurect the code!
Thanks for building this :D