Years ago, while playing to a 12, I shot an ugly 46 on the front nine. I told my partners I was skipping the back and going home to nap. They convinced me to stay. I shot 33 on the back.
My answer is "Yes & No"
No, if by "belonging" to a course means you get special privaleges at a semi-private. My experience is that you are still faced with difficulty getting tee times, (especially on weekends)...
Got my first hole-in-one today. 120 yards to the pin, hit a gap wedge. Shot 79 with 3 doubles and two 3 putt bogies. Not bad for a 11.5 index. Had to tell someone.