Is an AAN required for a Line of Credit that is tied to a deposit account to cover Overdrafts if for whatever reason the Bank refused to cover an Overdraft with an advance on the line?

Huh? If you haven't terminated the line, how can you refuse to advance?

One example I can think of is let's say there is a limit on the Overdraft line, such as $1,000 and the transaction would push it above that. Not sure of other situations I can come up with, maybe if the Bank thought the Overdraft was from a fraudulent transaction and so declined to process and advance the funds. Maybe this isn't a valid question. But, if for ANY reason, an advance was not allowed, is this Adverse Action under ECOA?

If you do anything outside of what your current legal obligation allows you to do - yes.