After you submit your application, Amex will give you a pop-up telling you clearly that you are not eligible for the bonus, and asking you whether you want to proceed with the application anyway.

There are even two separate pop-ups: one for someone who has already gotten the bonus (Amex’s ‘lifetime limit’ rule), and a separate pop-up language for someone who has never gotten the bonus but is ineligible for the bonus due to having applied for too many cards or whatever other factors Amex considers.