We did and it stayed on for most of our trip. I think I went over it around day 7 or 8. Actually had enough room to put both mine and my husband's numbers.
I've mentioned this in a few other threads, so sorry if it is a repeat, but besides the phone number thing, and recognizing a cast member, teach them to find something to go to immediately if they get separated from you. We taught my daughter, who was also 4, to find a trash can since they are placed every 30 feet inside the parks. We figured 1. it gave us all a point of reference and 2. it seemed safer than telling her to just go find a cast member. We never had to worry if it would have worked in that situation (thank goodness!) but she did remember the rule very well and pointed out trashcans all over the place lol