Hey Paul, hope you're well.
The docs indicate what the "supported" upgrade paths are...indicating those that our engineering and QA teams have tested extensively in various scenarios, across multiple OSes, etc.
I can't say for sure whether 2.2.0 directly to 4.x will definitely work, but I don't believe there are any specific restrictions in the product to disallow it.
Your "best practice" path would be to upgrade to the latest 2.5.x and then from there to 4.x.
One thing to keep in mind about going from 2.x to 4.x is a change in how our client libraries bootstrap off the cluster. I'd actually recommend upgrading to the latest version of the SDK if you haven't already as it will be backwards compatible with the older server version and likely give you a smoother upgrade experience.
Do you have an EE license with us? If so, I'd recommend getting in touch with support so they can help you through the process. If not, we'll do our best here :-) Regardless, I'd recommend testing out whatever path you choose in your own environment with your own data/applications.
Hope that helps, let us know what else we can do or if you run into any trouble.
Perry