Legally speaking it probably wouldn't fly since it is an obvious attempt at not having a real "private club" but more a means of circumventing the law.
Here is a piece that details some of the considerations as to whether something is truley a "private club" (legally speaking) or not -->> http://www.cmaa.org/uploadedFiles/PC...une02legal.pdf
1. Is "club" truly selective in it's membership and are such criteria enforced.
2. Are membership rules not structured to simply evade other non-discrimination laws.
3. Does the organization advertize for general/random membership or for the delivery of goods/services to non-members.
4. Size can be a consideration.
5. Who controls the organization, is it truly controlled by the club members through an elective process or is it controlled by an individual "owner".
6. Who controls the funds of the organization, are they controlled by club members through member selection process or are funds controlled by an individual "owner".
7. Is the "club" operated for profit of an individual "owner" or is it operated for the benefit of the members.
For profit businesses trying to evade the law by claiming they are a "private club" probably doesn't work very well.