The problem with this approach, is that once your dial-up connection is created, the alert that tests if you can ping an external IP will not fail any more, so either your dial-up connection will hangup, and you will get a whole series of alert email as the alert fails and succeeds in a cycle with the dial-up connection, or the dial-up connection does not hang up, in which case the whole alert will become useless, as it will just end up testing the backup dial-up connection instead of your main one.

There are monitoring systems like nagios that can be configured to only send emails if the ping status changes.

Now if the link goes down, it'll send an email, which the local mail server will hopefully keep in its spool until the second link is up again, and then send it. When the link goes up, the monitoring system will issue a second mail. If you're familiar with the setup, you know what that means (ie that the backup link works). So I don't really see a problem here, at least if the system is configured properly