I think it would be a good idea to wait until the DD is finished (or at least getting there) before going too deeply into the core. Otherwise you end up with hacked-up code because some idea suddenly doesn't fit into your previous concept of how things should be.
Thats my experience from when I was younger embarking on larger projects without any planning
I don't think that the Networking side of thing really depends too much on the core. I mean, the data, yes, and what it sends, but those are just "things". What to send, when to send it, total throughput, server loadings etc are (IMHO) things which the Networkers need to consider.
For example, in the example Hellfire has produced, we have an object called Map, and the information from some set of co-ordinates is sent. Regardless of what the Map turns out to be, we have some concept of what needs to be sent and when.
Naturally overlap is good, because the server requires the core and networking and the cilent requires the GUI, networking and fragments of the core. (or does it? This needs to be thought about)