I usually check email in the evening before going to bed. It's working marvelously since I can take an hour out of my day to handle everybody - really solves the problem of forgetting to respond to people. The only problem are time-sensitive emails. For those I still need to periodically check my inbox to see if something urgent's come up. If there's a way to tell Tray "If time-sensitive email, send me a tweet", that…
The idea would be that you could setup custom rules based on the people who email you, or other web services you use, for example if a hot lead in sales force emailed you while your in a meeting, then forward it via SMS.
Being able to pickout a "time sensistive" email would really depend on what you consider time sensitive, but im sure we could provide something that would help.. email dom at tray.io and we can talk more about how tray could help fix your issue..?