Sure, this will often happen if litigation can set some precedent that benefits the profession as a whole. For example the AMA will take up cases that can challenge legal precedent on malpractice damages limits. Sometimes these disputes can be with management, but generally these kind of interventions are done as part of professional advocacy.

However a professional association is effectively limited in what it can do in a labor dispute because management has no obligation to collectively bargain with them, hence this is not really the purpose of professional associations.