I don't believe so. The actual card is managed by Chase, payments go through the Chase website, etc. Amazon just links to it and updates your reward balance nightly.
Note that it's better if you don't apply rewards points at checkout - instead, get a payout to your bank account via the Chase reward redemption portal in the app. If you have $100 in rewards points, and use them in checkout, that $100 doesn't hit your card and you don't get the 5% cashback on that $100.
Technically you don't even need to loop through the bank account, you can also do statement credit. It doesn't count against your minimum payment, but it does count as a credit/payment towards the statement balance.
But yes, always charge the full amount and then handle rewards at a lower layer, never "pay with points".
Sure, to get $100 in rewards you'd need to have spent $2,000. It's not life-changing but $5 is still something, and I imagine Chase/Amazon save >1 million a year from people not doing this.