In my experimentation with this tool I used to confirm that this new headless browser Googlebot seems to accept and store cookies, and send them back to your server too (as well as referrer headers).
So now the trick was to check whether Google would really store and return this cookie. I ended up settling on a simple setup with a PHP script that set a cookie and output an page containing an iframe, the document in that iframe was a second script which output the HTTP headers Google sent with the request:
You can see that sure enough Googlebot sends back a Cookie header with the value I had set in the ‘outer’ script. It sends a Referrer header too.
What does this mean?!
So far it is too early to tell. Google doesn’t keep the cookies between runs of the tool, so it really depends how they treat things when actively crawling pages. If crawling multiple pages like a single run of the tool then we should see cookie affected results appearing in the index, but it might be that Google crawls each page separately in a different ‘session’ and then this won’t change very much.