Oh come on, email rarely takes 20 minutes. Even if it did, the best thing to do is send a message both via SMS and email to maximize the chances that the largest number of people will see the message. If one more person sees the alert because they got the email and not the text, or even if they just see it earlier, it's worth it. That's how it worked at my university. 

Email is relatively cheap to send, and mass SMS systems can be plenty finicky on their own.