Does Gmail provide a way to see a hash that they say represents the sum of all data within a given email?
Not exactly a hash, but every email has a unique ID. This value is accessible through the
X-GM-MSGID email header.
This value, when converted to base-16, is
143ff493385c94e5, and with this we can directly link to said email: https://mail.google.com/mail/u/0/#inbox/143ff493385c94e5. (note: that link won't actually work unless you're logged in as me)