Time-sensitive is so subjective that it'd be difficult to say the least if not impossible to properly implement. The only 100% guaranteed way of making sure a rule gets applied to time sensitive emails would be to train senders to add a word or code to the subject or body of the message. But again, this is based on my subjective definition of time sensitive. To me, time sensitive means someone I know sends me an email and they need a reply or at least my attention right away. That leaves out things like leads coming in from NetSuite or Salesforce (as mentioned in other replies) or automated emails that cannot be trained. It also means that I'd have to train a lot of people to do this and I may leave out some people by accident and then I'd have to train every new contact to do it on top of deciding whether or not the contact is important enough for me to allow them to send me emails that'll alert me instantly.

There's just so much to it that it seems like something only a human could do. That said, the guy from tray.io who replied with a potential solution seems to be on the right track. Its not a perfect solution but it's good enough and sometimes good enough is all you can do.