I don't see any reason why not. Several pilots here bought their first plane while they were students, and trained in them, and took the checkride in them. There was a thread about it not too long ago.
I think it's important for the manager of a "social club" such as a flying club or country club or community pool to have a passion for the area the club focuses on, but not necessarily be participant. The general manager at our country club is not a golfer.
Is your CC manager drawing a salary? Despite not being a golfer, he's presumably a diligent person who does a good job of managing the operations. If he's not earning a respectable salary for his efforts, he probably should be. On the other hand, most people look to a flying club or partnership to reduce their cost of flying, by sharing fixed costs with others, and eliminating the overhead/profit of an FBO by substituting sweat equity.
Yes, a pilot can buy their first, last and only plane (whether HP, twin, etc.)
ab initio, train in it, and fly the wings off it happily ever after. There are some advantages (train like you fly - better familiarity with the ship), and also some added expenses doing it that way (ins. costs, more inst. hours required, safety pilots, solo/pax restrictions). There's also constant discussion on this and other boards about the tension between buying a plane sooner (skill-appropriate 172 or PA-28) and buying the kind of plane will suit the mission as a pilot's skills grow (complex, HP, 6-place). If one buys too soon, they can buy the wrong plane.
As for the non-pilot starting a club, before I considered joining I'd want to know more about the individual's motivations, and how the inevitable work of managing this club is going to be allocated. If it turns out the individual is just setting himself up as a fractional GA ownership manager, that can work too, but again usually does not provide the cost advantages that many private pilots look for in joining a club.
