For G Suite.
Is there a way to disable the Gmail "Get the Gmail app" screen for mobile users?
There is no such way.
The Secure browser displays the Gmail screen for the mobile users.
This is the screen which the Google intendedly displays on the Gmail screen for the mobile users to urge the usage of Gmail application.
This page definitely appears regardless if you use the secure browser or not.
It is available as it is by clicking the link [mobile site] shown at the bottom of the displayed screen.