No, this is wrong. The authentication cookies for GMail are named "S" and "GX". They're both set only on "mail.google.com", and they both have the secure flag

No, this is wrong. The authentication cookies for GMail are named "S" and "GX". They're both set only on "mail.google.com", and they both have the secure flag so they're only transmitted over SSL. There are certainly other Google cookies that let them track your identity that will get sent when you search. But those cookies are not sufficient to get access to GMail.