Does Time Machine back up Mail's Inbox?

I just discovered that something happened to my Comcast email account and all mail older than 45 days was deleted. I had moved some of the messages into "On My Mac" mailboxes, so those are still okay, but everything else was lost. I don't use that account a lot, but still, I'm not happy about losing mail.

I searched in Time Machine and couldn't find a sender I knew had been in my Comcast mail. Am I correct that Time Machine does not back up the Inbox, instead relying on the providers' remote email servers to retain messages?

If I'm wrong, how can I find my lost Comcast messages within Time Machine?

Thanks!