Can I deploy a SharePoint Add-In with User Profiles (Social) | Read to the SharePoint AppStore?

you can not get the propties of a profile where you have not the right to see it.

var clientContext = new SP.ClientContext.get_current();
var peopleManager = new SP.UserProfiles.PeopleManager(clientContext);
var personProperties = peopleManager.getMyProperties();
clientContext.load(personProperties);
clientContext.executeQueryAsync(function () {
// First time experience completed
var prop= personProperties.get_userProfileProperties()['prop'];

a example above. and please be aware you need to us  SP.SOD.executeOrDelayUntilScriptLoaded