That's very odd that they wouldn't help you with getting on their network. The networking components of XP Pro and Media Center Edition are identical because they are the same OS. Anyone who tells you that they differ by anything more than a few additional apps don't know what they're talking about.
Change the task bar color from MCE's nice-looking default blue to silver or green, delete the Media Center app shortcuts from the Start\Programs menu and few would even notice it's not XP Pro unless they looked at the Systems Control Panel, which identifies the OS.
What exactly do you need to get configured? You need to be on their network as part of their domain? Or do you merely need to configure your system to get access to their wireless network?
If it's to be on their domain, you're probably out of luck since it takes a systems administrator with the appropriate password to put your machine on the domain. So instead of being on a workgroup, your machine would be placed under Active Directory with all the permissions and policies of the domain. Sometimes your machine has to be on a domain to get access to resources not available to guest computers.
I would doubt that's what they mean, though. Few businesses or institutions would permit ANY strange computers onto their domain that aren't under the tight control of their IT department. Personal computers tend to have non-approved apps and are are higher risks to get spyware or viruses. So exactly what does it mean to get access to the network?
If it's just getting an IP address off of a wireless network, just tell them you have XP Pro and ask for the SSID and password/encryption method to get on the network. They would never have to even see your computer.
As for your question about whether you can use XP Pro's upgrade CD, the answer is no because you're essentially cross-grading and not upgrading, so the installer wouldn't permit it. Of course the whole thing is really dumb because there are no differences network-wise between the two OS versions.
