You can't send an SMS directly from the program, you can only compose a message but the user would still have to click "Send". The same applies to sending an email.
You can use an existing (or set up your own one) web service to do both of those things for you and just call the service from your wp7 app.
If it's just alerts you want though, I had good success implementing my alerts through Twitter using TweetSharp . The app would post a little note under a set up twitter account and the guy receiving the alerts can subscribe to that account and have the alerts pushed to him with minimal latency. The functionality doesn't require any user activity (like clicking "send") and can even be fired from a background task.