Since some people asked, I called Chase back and talked to someone else. You were right that showing the CSR does not get entry. She told me that if you charge entry to the CSR, they will refund two of those charges per calendar year (presumably, this is only an issue right after you get the card, or if you somehow forgot the CSR, but had your PP card with you).

It does count against the travel credit (if the lounge is classified as travel), but they will also give you the refund, which makes up the loss of the travel credit.