A question about adding a Gmail account in Mail

This is Cory. I want to ask this question. Whether you have an Apple account associated with your Google address or not, when you add the email to your iOS device's Apple Mail app and select 'Google', you wouldn't get an email from Apple itself wouldn't you, only from Google?

This would be so, if you have never had or are no longer using an Apple ID, whether deleted or signed out. Also as such, the iOS device of which you would login from, wouldn't not be linked to any Apple ID device information - if the Gmail login was strictly for the Mail app only and not to login with the same email for iTunes, since Apple and Google logins are different from each other.

Am I completely right?