Will removing the 'mktNoTrack' class from mailto: links prevent them from being included in link reporting?

It's actually the opposite. If you add the "mktNoTrack" class then the link will not be converted to a tracking link. It will appear in the email as-is. If there is no class attached then the link will be converted to a tracking link and you will be able to report on clicks.

There is no technical way to report on a click without re-directing the user through a middle man. So, if you need to report on a click, you'll have to let it continue to be a tracking link. When the user clicks on your mailto link, it will open a tab in their browser briefly, then launch their mail client. If you choose to add "mktNoTrack" then the link won't be tracked and it will just launch their mail client without opening a tab in their browser first.

These are the only options, choose which one works best for you.

I strongly recommend adding the 'mktNoTrack' class.  As Justin notes, adding the class is how you turn off tracking, and you also vastly increase compatibility.

The operation invoked by a mailto: link changes depending on the mail client you're using. Some webmail interfaces, like GMail, rewrite such links so that they result in a New Message pane within GMail, as opposed to launching the machine's default (usually desktop) mail client .  This is good for user experience.  Other webmail apps such as Outlook.com will respect the original intent of the mailto:, so despite that fact that you're in a mail app when you click, another mail app (such as Outlook Express, Windows Mail, etc.) will launch for the new message.  This is bad: since that other mail app may not be configured to send mail, the lead is at loose ends.  Worst case: they think they sent an email, but it stays in the Outbox of their default app (which they never check).

Behavior like GMail's increases compatibility because it means no fooling with broken/unconfigured mail apps. Unfortunately, when you enable click tracking for a mailto: link, this makes the link an link.  Therefore, GMail doesn't know to do anything special to keep you within their app. As a result, you end up launching the probably-non-working default app. 

I hope the obviously common situation described above persuades you to to disable click tracking via 'mktNoTrack', even if it means less of a trail within Marketo (you do have their email itself as a moment, of course!).