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.

It depends on why you're checking emails. If it's just for password recovery, for example, then it's the user's loss if they intentionally use an invalid email.

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