You've described existing infrastructure, but the important thing for the business is applications. That's the thing they need, every day. I worked in an infrastructure group in a UK investment bank, the only time they notice what you do, is when it snarls up or fails.
For example, there was a recent thread discussing whether Access has an open-source equivalent, IMO it doesn't really. So, if they use a lot of Access that will constrain upgrade path UNLESS they're prepared to take some risks and spend to take it out of the equation. But, mainly, the list of what's delivered to the business via the servers and on the desktop is the thing. No-one cares about infrastructure [except us, boo-hoo] as long as the price is right [including manpower] and it works.
It sounds, to me, like this is Windows desktops and Linux servers [and therefore Samba, LAMP etc. for example] this is not a bad way to live and many companies do so. That would mean that the client upgrades and server upgrades would be reasonably orthogonal, but I don't know all the details, either. To be honest, I'd be inclined to ask this on Server Fault, but unless there were more details, it's likely to be closed as being 'open ended'. Good luck!