Most standard custom fields do work with the Address Book. However, if you have custom fields added by a plugin which are updated by javascript then the Address Book plugin will not always know how to handle the data. If you are running into an issue please post an issue in the support forum or on github with what plugin or code you are using and as much details as you can. We will determine if the Address Book plugin is able to provide support for the plugin or if a custom solution would need to be developed for your use case.