Did you see my post on our recent office break in?
Turns out we were not notified because we were, (no longer) on cellular only.
ADT's cellular monitoring is handled on a separate ATT network.
The night we got broken into the network was down nationwide, as in pretty much all of N America.
Fortunately the thief's were not aware so they left quickly assuming the cops were on their way.
Had they hung around for a few minutes they would have realized that we were blind and could have leisurely cleaned the whole place out.
I have peripherally looked into cell as a backup for my home system and what you can do is self monitor.
You can get an adaptor for your alarm system that will let you add a cell phone as a call out device. Add a second line, $9.99 with ATT, and dedicate it to that. Program it to call you.
Here's a good article.
Home security on your iPhone | TUAW - The Unofficial Apple Weblog