FUELnycdoes the code only apply to the item number but none of the "parameters" set up for it?
Yes, that is correct, with a couple other exceptions:
Changing the product's Item Number, Suggested Price (if you use "Let buyer edit price"), or Variants/Variations options would alter the button code and require replacing any earlier Add to Cart code for that product on your page. For any other setting changes, the existing button code in your page will continue working just fine. :^)