I'll take it one step futher - why get rid of Windows 7? You already have licenses, probably already have some patch deployment method in place, and your users are probably happy and familer with it. There is going to be a ZERO cost benefit of going from Windows to Linux because the company ALREADY HAS licenses. Now, if you are talking about bringing in future people, and in future computer purchaces, going open source, that is different.
All going from Windows to Linux is going to do is frustrate users, and going from Microsoft Office to OpenOffice is yet ANOTHER new Office product they have to use. You will have to incure a cost of training users, and suffer from a temporary loss in productivity while the users learn the new system. In other words, converting from Windows 7 to Linux will probably ADD costs, not save them. On top of that, you would have to incure the costs of reimaging your entire Windows user base, and backing up user data, then porting it over to Linux.
I say, stick with Exchange - your department has already sunk money into it, and leave your Windows users alone. Your solutions are going to COSTS money, not save it.
While I agree that it sounds like he probably shouldn't do it right now, your argument is wrong. Sure, they already have licenses for Office 2007/10 and windows 7. However, they don't have licenses for the next version of Windows and Office that they'll end up having to get when Microsoft eventually drops support for Windows 7. Many times you need to upgrade before support ends.
Also, what about the next version? And the next? And what about the future cost of trying to get all the old Microsoft Office documents converted, since they will no longer work with the latest version in 10 years.(Ever tried to open a Word document from the 90s in Word 2007/10? It isn't pretty. Hell, Libreoffice supports old word documents better.) Oh, and I guarantee that Microsoft will change the Desktop and/or Office GUI in the future, so you still have training costs. At least, my organization spent quite a bit of money training users on Windows 7 when they moved to it.
Basically, here is my point: Migrating to Linux will likely cost more and cause more frustration in the short term. However, it will save money and save frustration in the long term. (Especially if long term >= 10 years)