Can you use an app specific password for Gmail set up with iPhone mail app?

The article that you posted from -- Using app-specific passwords - Apple Support -- is about using Apple app-specific passwords to access your Apple account; for example if you have iCloud email and want to access that from a non-Apple application such as Windows Mail.

If you want to add Gmail to your iPhone Mail app, that article would not apply. To do that, see the following from https://support.google.com/a/answer/9003945?hl=en#zippy=%2Cset-up-gmail-with-the-mail-mobile-app%2Cset-up-gmail-with-mail-on-a-mac

If you’re using Mail on a mobile device, follow the steps at Add an email account to your iPhone, iPad or iPod touch, on the Apple support site. 

Important: When you’re asked to select your email provider, select the Google option.

Regarding using Google App Passwords, see the following from https://support.google.com/accounts/answer/185833?hl=en

Tip: App Passwords aren’t recommended and are unnecessary in most cases. To help keep your account secure, use "Sign in with Google" to connect apps to your Google Account. 

and

Tip: iPhones and iPads with iOS 11 or up don’t require App Passwords. Instead use “Sign in with Google.”

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