Can an AM Adult Standards station,with no FM presence, that is supported by donations from listeners be successful? The answer is YES. And I will offer proof of it.
WAVO Charlotte, NC was part of a 3 station cluster owned by a religious broadcaster. WAVO would play Adult Standards beginning at 10am, first airing the Bill Bennet conservative talk show, then sign off at 10pm, I believe. Nighttime power was only 60 watts, and didn't cover the market. Well, one day the owner went on the air and announced the format was going to end, as the company no longer wanted to foot the bill, as it was never profitable from day one. He did offer a solution, if enough listeners donated to reach the amount (I don't recall the dollar amount) needed over the course of a year to run WAVO, it would stay exactly the same, and still air Bill Bennet. They not only reached, but surpassed that goal. This model continued for awhile. But due to the owner's age and health, he had to exit the radio business and sell all the stations.
Two current, successful examples, are WKHR, a non comm FM Big Band/Standards that rimshots Cleveland. And a personal fave that I have donated money to, over the years, is KNCT-FM Killeen, TX, as they are the last "true" Beautiful Music that streams at no charge. KAHM's stream is a monthly $10 subscription fee.