On gogo wifi right now and I'm not able to replicate the results. After paying for access I've tested several google services with no certificate issues(checked with latest Chrome, and openssl's s_client).

I opened another laptop(I travel with two), and without paying I started testing outbound connections with openssl's s_client and curl. It appears that the gogo wifi system will allow between 5-10 ssl connections before starting to block all outbound ssl connections. Without paying all http requests include a redirect to the captive portal, but at no time did I see a self signed cert for any of the https connections attempts.