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?
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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.