Auto Pay Bank Credit card with Fidelity Brokerage Account?

I hold multiple credit cards from several banks (such as Chase, Capital One, etc.). Instead of linking these cards to my savings account, I'm considering linking automatic payments (set up auto-pay at the bank/credit card end, rather than through Fidelity's billing process, since Fidelity doesn't know my monthly balance) to my Fidelity Individual Brokerage account. I think this is a reasonable move because Fidelity's core position(SPAXX) typically offer higher returns than High Yield Savings Accounts (HYSAs). However, I'm concerned about whether this will achieve the desired results and whether there are any potential issues with this setup.

Assuming I always ensure I maintain sufficient cash in my Fidelity account, is it possible to link my Fidelity brokerage account to my credit cards, wait for the automatic payments to complete each month, and then leave it at that?