Yes.  The determination of whether a nonprofit organization qualifies for 501(c)(3) charitable exempt status depends on what the organization does, not who controls it.  That is evident from the fact that the IRS has granted (c)(3) charitable exempt status.

The structure of the organization should answer my favorite question of “whose organization is it?”  (See Ready Reference Page: “The Key Question—Whose Organization Is It?”) For-profits often create their own private foundations.  Community groups (501(c)(4) organizations) and trade associations (501(c)(6) organizations) often create charitable arms to carry out charitable programs in which they have an interest. If the club wants to have full control of its charitable arm, it should have the right to appoint—and to remove—the members of the board.

The key administrative issue is to be sure that funds of the charity, which are often donated and deductible as charitable contributions, are not used to promote the non-charitable activities of the controlling entity for which donations would not be deductible as charitable contributions.  If the IRS were to determine that the controlling non-charitable entity received more than incidental benefit from the charity, it could revoke the charitable exemption of the (c)(3).  Reasonable operation as a separate entity and reasonable precautions against private benefit should allow the charity to keep functioning and retain its exempt status.