I ask because I connect to Gmail over HTTPS and if emails sent from one account to another (or the same account, just to back something up) don't actually leave Google then it's end-to-end email encryption.
Is this the case?
It depends on the network setup Google has. You can check the route your email took by checking the message headers. In GMail, you can do this by:
Look for the
Received headers. Those identify the email servers that handled the email.