The Disney parks have very good procedures for dealing with 'lost parents' (CMs have said they never say the kids are lost because kids stay more calm if they think their parents are the 'lost' ones. Plus, from the child's point of view, the child is not lost, he/she knows where they are).
From what I have seen, CMs with scanners have access only to the information they need to do their jobs. So, a CM at an attraction scanner may only have access to the name and the Fastpasses.
As a previous poster mentioned, kids who have lost their parents are brought to a central location and lost parents are sent there. They certainly COULD have a reader there and have access to contact information from your account. I'm not sure if they do or even if they would use the information because there are a lot of variable - like what phone number is linked to your account. If it's a home number, that wouldn't do any good. Even if it's a cell phone, is the person with that cell phone number with the child at the park today?
With all that, it is probably faster just to send lost parents to the place the child will be brought.
When putting contact information on your child, you may want to think about who it would be visible to. So, you might not want anything that's too easily seen, but also keep in mind that CMs can't remove clothing to find it (you can teach your child to show it).