It's a good idea....A really good idea... They will still look for you if they just have an alert but.....
It means when you accidentally set it off you get a phone call (surprisingly quickly), and you can avoid wasting the time of the folks who may some day save your life.
If they don't have a phone number they have to figure out if it is real or not. Best case the beacon is reporting at a controlled airport and they can call the tower and ask if they are missing any planes. Then someone has to walk the ramp listening for beeps.... Worst case they have to dispatch an aircraft to try and locate the signal. Lots of money and resources wasted.
Here in Canada being not registered means they don't know you are an airplane needing help making it a police matter rather than military. The police have fewer resources.
If you are looking for the reg... NOAA says:
Failure to register, re-register (as required every two years), or to notify NOAA of any changes to the status of your 406 MHz beacon could result in penalties and/or fines being issued under Federal Law. More importantly, failure to maintain accurate and complete information could result in a delayed response by rescue forces. The owner or user of the beacon is required to notify NOAA immediately of any changes to the registration information at any time. By submitting this registration the owner, operator, or legally authorized agent declares under penalty of law that all information in the registration information is true, accurate, and complete. Providing information that is knowingly false or inaccurate may be punishable under Federal Statutes. Solicitation of this information is authorized by Title 47, Part 87 of the U.S. Code of Federal Regulations (CFR) and the U.S. Office of Management & Budget (OMB) Control Number: 0648- 0295.
