He's free to challenge the rules.....but I don't think he has a chance in hell of winning.
His actions UNDOUBTEDLY damaged the league. Of this there is no question or debate. The other owners and league has every right to remove him.
In terms of the private convo, that is irrelevant. The NBA didn't obtain the convo illegally, they didn't do anything but react AFTER it was made public. For that to be relevant here it would have to be proven they actually had something to do with making that private information public, which they did not.
You may very well be right re: him having very little chance of winning. But to say so with any certainty is foolhardy at best.
You are banking this strictly on the NBA by-laws which are not the law of the land. It doesn't matter if his comments damaged the league and it doesn't matter how the NBA got their information. What matters is whether or not the NBA's by-law can stand up to legal scrutiny or not. That's it. Nothing else.
Assuming this goes to court, the NBA will argue their case and Sterling's lawyers will argue his. A judge will then interpret the law and determine whether or not the NBA can legally remove him from ownership. My guess/hope is that the judge will rule in favor of the NBA. However, I wouldn't even bet my vcash on it. Especially since it will be tried in California.