Here's what will happen: Every project's business sponsor in the company will find out that his/her project is being delayed. They'll express their concerns, with greater or lesser emphasis and heat, to the CIO. Assuming he's read more of my writing than just the fix-the-help-desk phrase, the CIO will recognize that he's fallen victim to the "optimizing the parts suboptimizes the whole" trap.
Or he'll figure out his priorities have become unbalanced, or he'll search for a scapegoat, or he'll call his managers together and tell them to work together more effectively, or he'll do something else that's face-saving and will let you go back to figuring out your own priorities.
Here's what you shouldn't do: Try to persuade anyone that the current situation is a problem using evidence and logic. That will put the spotlight on you as a troublemaker who can't get the job done -- exactly the wrong focus and something that will prevent resolution.
This advice, by the way, is an example of a broad principle that applies to a wide variety of circumstances: When employees are too effective at hiding the consequences of bad management decisions, they act as enablers and do nobody any favors. It's generally a good idea to let just enough negative consequences leak out that those who need to know have an opportunity to recognize the bad decisions for what they are.
Oh, one more thing. Don't be too hard on the help desk manager. She's doing what she's paid to do, which currently is to play the game to win. It's up to the CIO to change the game.