
Hello,
They should not see the “unverified app” message if the application is whitelisted. We can confirm this by reviewing this Gsuite updates documentation which I understand is not the clearest but it does states that after july 8, New users will not be able to install unverified apps unless you “trust them” which would be whitelisting. Hence, after whitelisting, the “unverified app” message should not be displayed.
Trust apps that you want to allow users to continue to install: To trust an app, use our API Permissions (OAuth apps whitelisting) feature in the Security section of the Admin console. Trusting an app also means that, if users consent, the app will have access to some G Suite user data (OAuth2 scopes) that you’ve otherwise restricted using this same tool. For example, if you’ve generally blocked access to Gmail OAuth2 scopes, trusted apps will have access for accounts where users consent.
If you have customers (users) accessing the app, then it should be verified, whitelisting on their behalf doesn't change that your app isn't verified.