+1 This
95% of the industry is using Windows and Exchange/Outlook. All of the peers that your management will run into use them. All of the vendors that provide possible software or tools for your industry expect you to have them. Also, if you can't properly and easily manage Windows 7, with all of the great management tools and Group Policies that are available and information online and from Microsoft Press, it is a failing on your part as it is a great OS and I've had a great experience with it in a very large company (~2500 desktops).
If you do this, I can guarantee they will be sold on or want to do something and then you'll have to tell them that it can't work in your environment. They may want to hire somebody and have a hard time finding a person with the requisite Linux experience and/or will have to pay a fortune compared to the army of people with MS experience. A customer or vendor will expect to interact with them via Office 2010 documents and it won't work right. Every new employee will stare at the PC with a strange look and say "this is different from what I know." They will ask why. You'll say it was because of your decision to switch to Linux to save a pittance on licensing. They'll reply that none of their peers at other companies have done the same thing so why did we do that again? It will be your fault. Over and over again. Forever.
At the very least, you need to quantify in your business case all of the flexibility that you are taking away of any future IT decision by dumping the Microsoft OS ecosystem so everybody understands that from the beginning and can't pretend like they didn't later.
People really don't get fired for choosing Microsoft - especially on the desktop. At the end of the day it is the industry standard and "best practice" and since everybody else does it they can't point at you in the event anything goes wrong and make out like you did something crazy/stupid choosing it which makes you grossly negligent in your job.