It would depend on what the agreement said. Regardless, try and leave while owing money and with all the club property you can get your hands on and see how they react.
No it wouldn’t. The provision of any given agreement may be found nonbinding if it is shown to be unconscionable. First semester contract law. Being forced to live under tyranny is the epitome of unconscionable contract. Therefore, it is inherently unenforceable, as a matter of law, the military calculus not withstanding.
Furthermore, freedom of association implies the right to quit any voluntarily entered association. You are right that consequences might follow, such as unsettled debt, and they must be attended, but the right of association (or lack of it) remains undiminished, as to our hapless country club member.
Extrapolating that right to the states is not that difficult. BTW, I didn’t see your post dealing with the rather persuasive argument that the Constitution is not a suicide pact. I am interested in your opinion.
Remember, long ago people referred to this country as "these United States" and not "the United States." It is a willing association of states based on common protection and interest.