Firefox's BrowserID/Persona used to do something similar. If you were logged into an email account (which supported it) and you signed up for a site (which supported it), it would auto-confirm your email. I never saw it in the wild, but the demo was awesome.

I wish browsers found an easy, secure way to bake this into the product. I'd much rather a confirmation modal than having to go to your email and click a link.

Not a great idea since it would require trusting the client unless I'm missing something.

This check only works client-side, so you can't trust it to protect against spammers.