Technically no. The collective bargaining agreement prohibits it. However a player may own shares of any publicly traded company which also owns a team (Note: not just any corporation, it must be publicly traded). If the player owned more than 50% of a publicly traded company, and that company owned more than 50% of a team then he would effectively own the team and it would not be in violation of the rules.
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In theory he could, there would be nothing stopping him, as long as he is a registered player with the club.