Not slightly, but humongously ridiculous
Now imagine plopping a Linux desktop onto these machines. Suddenly there is no support; the dev teams have to be replaced/retrained because they don't write code for Linux; the help desk workers have to be replaced/retrained because they don't know Linux. The desktop user is confronted with an unfamiliar environment with unfamiliar tools and applications, and since the tools they were using are no longer available, they cannot get any work done.
You couldn't come up with a more ridiculous way to do that, could you?
The sensible way to do it is of course in the exact opposite order: First you train your developers and support staff (or get new ones), then you train your users, and only then do you switch everyone's desktop over.
And with many corporate apps living in the browser nowadays (not that I otherwise endorse this development, but this is the one aspect of it that may be useful), there's that much less retraining needed for end users of those apps. Not that re-learning the same app on another OS should be all that hard either: Menus are menus, file-opening dialogues are fairly self-explanatory on most OS GUIs, and so on. How many weeks' retraining would you need ro switch from, say, MS Office Mac to MS Office Windows?