Absolutely! Never forget that all e-mail lives in on-line servers. In order to securely handle them you should set up your e-mail client to download e-mails to your machine and then delete them from the server. If you want you can let them live for a week so your mobile devices don't get into a catfight.
If your computer, laptop, tablet and cell phone are all set up to download and delete from server, the first device that grabs it is the only one where you can see the e-mail. It becomes a game of "who hid the cheese." So let them live for a minimal amount of time to ensure that all devices have the same e-mails and then delete them with a schedule on the server.
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