If a page is unpblished are any links on it broken or lost?

 Specifically, I am dealing with cards being tested through my site. I added a Captcha but am unsure if that will solve the issue or if it is even working.  I temporarily want to unpublish the index page in hopes it breaks the automated transactions (they show as suspicious from the credit card processor). I am wondering though since the payment button is on the index page that takes you to the processor site will that be dropped, broken or lost if I unpublish.