Can I update from Lion Server to Mountain Lion Server through Remote Desktop?
Basically, I think the answer is Yes if your server has an static IP, and your client is on the same network.

But that's in theory of course. For example, if both your computers are in a network without DHCP, they will assign themselves with an IP starting with 169.254., link-local IPs. Now, the computers know that each other exists, and can still connect to each other with that IP.

Now, the question is simple, you need to know what your server's IP is when the DHCP is gone, and no one can assign IP address to them. And since you won't know, put a static IP on, and it would work.

That's in theory again. But I've had situation like these, and it did work for me.

Anyway, good luck!