will iCloud backup my emails?

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Your iPhone, iPad, and iPod touch backup only include information and settings stored on your device. It doesn’t include the information already stored in iCloud, like Contacts, Calendars, Bookmarks, Mail, Notes, shared photos, iCloud Photo Library, My Photo Stream, and files you store in iCloud Drive.

How to use the Mail app on your Mac to move, delete, or copy iCloud email​

Copy email from iCloud to your Mac

1. In Mail, choose Mailbox > New Mailbox.
2. A New Mailbox dialog opens. Choose On My Mac from the Location pop-up menu, then enter a name for the new mailbox. Click OK.
3. Select your iCloud inbox from the list of mailboxes in the sidebar, then select the messages.
4. To copy messages, hold down the Option key while dragging the messages you selected to your new mailbox. Or choose Message > Copy to > your new mailbox.

If you want to make a backup copy your entire iCloud mailbox, including every message and folder in the mailbox:

1. Select your iCloud inbox from the list of mailboxes in the sidebar.
2. Choose Mailbox > Export Mailbox.
3. Choose a destination folder for the mbox archive, then click Choose to save it.

No, your Mac emails are stored in iCloud, but are not "backed up" per se.

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