Upgrades are assigned by each individual hotel. Every hotel (even corporate-owned and operate ones) are separate businesses. Since hotels receive nothing when a guest signs up and/or uses the chain's credit card, they aren't going to care what type of card a guest uses.

I have no direct knowledge about the Property Management System (PMS) used by Marriott. But, none of the various PMS I've seen provide information on which bank issued a given credit card.

In that scenario, the only way a Front Desk staff member would know you are using a chain-branded credit card is if you physically hand it to them (and they look). Or even less likely, the staff member would have memorized the common sequence of numbers for the card. (I want to say that the first 7 digits of a Visa/Mastercard can be used to identify the issuing bank. But, it's been a minute or two since I've needed to know that information, so don't quote me.)

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TL;DR: The likelihood that using a chain-branded card will help with an upgrade are close to zero.