They can sue yes, less likely to win. Modern courts really don't want to second-guess management strategies, and instead focus on things like fraud, conflicts of interest, and misrepresentation. If the company openly said that they are going to pursue policy X because they think this is in the long-term best interests of the company, and some shareholders sue to argue that it isn't, courts are rarely going to step in and try to determine that management should've pursued some other strategy. For one thing, they aren't really equipped to determine what would be the right course of action (valuing things like "goodwill" is not really an exact science), and for another, shareholders already have a mechanism for resolving those questions among themselves: shareholder votes.
Instead, to win a shareholder lawsuit you usually need much more of a smoking gun, things like being able to show that the CEO pursued a certain deal because his brother owned the other company, or that a group of controlling shareholders are having their chosen board take certain actions that deliberately screw over minority shareholders, that kind of thing.
