I spent 7 years working with digitalisation in the Danish public sector and it depends on what you mean, and what you want to pay for it. Basically the short answer is that it is impossible.
What is often forgotten about non-tech enterprise here on HN is that a typical public sector organisation has a ratio of 20-50 IT people (this is everyone, from the network and operations people to developers and project managers) per 10.000 employees in organisation where almost every employee uses some form of IT system to perform their duty.
Some users will not be capable of telling you if they are on an iOS or Android devices, and almost all of them know Microsoft Office and Outlook because that is what every place they have ever worked and will ever work uses. Or to frame it differently, the change management and retraining of 10000 employees is going to crush you, very, very quickly. On top of that your IT staff is certified and trained with Microsoft technologies, and most of them are likely happy about that to the point where they will leave your organisation if you push them toward Linux.
That is the employees. There is also the technology, and all the IT systems that only works on windows and have no competitors. This can be everything from your million dollar MRI machine to the dentist program (dentists are part of the public sector in Denmark). Cutting ties with Microsoft completely, would mean you’d need someone to develop alternatives to these things. (Yes, your million dollar MRI machine shouldn’t depend on windows XP, but it does).
So obviously it’s not impossible, nothing is, it’s just really, really, expensive. It’s so expensive that it will likely be it would be political suicide because the money you need to pay for the transition is going to come from firing nurses, school teachers, and other primary functions.
That being said, a lot of public sector organisations do take open source seriously. Especially here in Europe. But there isn’t a clean way to cut ties with Microsoft, and it’s actually become harder and harder. Because where is the Linux alternative to office365?
Disclaimer: I consider Microsoft to be the best external business partner that I’ve worked with while I was in the public sector.