It seems like Elon could win a suit to the extent that he could get all of his donations back based on the emails soliciting donation for a purpose that was then changed.
But Elon's goal in this suit is clearly to bring back the "Open" in "OpenAI"- share more information about GPT4 and newer models and eliminate the Microsoft exclusive licensing. Whether this would happen based on a suit like this seems like it would come down to an interpretation of the Articles of Incorporation.
The Articles of Incorporation are going to be the key legal document. Still, the Founding Agreement is important to demonstrate the original intentions and motivations of the parties. That builds the foundation for the case that something definitively caused Altman to steer the company in a different direction. I don't believe it's unfair to say Altman is steering; it seems like the Altman firing was a strategy to draw out the anti-Microsoft board members, who, once identified, were easily removed once Altman was reinstated. If Altman wasn't steering, then there's no reason he would have been rehired after he was fired.
Subject to limits on specific kinds of contracts that must be reduced to writing, all US jurisdictions (not just some states) recognize oral contracts provided that the basic requirements of a contract (offer, acceptance, consideration, etc.) are present.