I don't have played Starcraft II, but I've worked on many RTS as a network programmer, and I'll try to give you a possible explanation of what is probably happening. When designing the network code of an RTS, you have two major options to do it.
The first option is to have each machine managing some subset of the units (those of the local player and maybe one AI controlled player) and to send to each other machine the modification of the state of each of those units (where are they now, did they change the currently playing animation, has their PV changed, ...). If you do it this way, you reduce the actual work of each machine (only compute modification for some of the units), but you increase the bandwidth used (since you have to send all modifications).
The other alternative is to have each machine simulate the behavior of every units, and only send between them the order given by the players since you can reconstruct all the state modification from that. However, the load of each machine increase. Many games (Warcraft III, Starcraft, Supreme Commander, Age of Empire, ...) use this model as it greatly reduce the bandwidth required. We speak of a synchronous network engine. I suspect that Startcraft II also use this model.
So how can a bad GPU cause you to lag ? Well, when you have a synchronous network engine, the timestep of the simulation processing has to be the same on each machine. So the slowest machine in the current game is the limiting factor. Moreover, the simulation and the rendering must be somehow synchronized (the rendering depend on the simulation, and you can't tell the other box you have finished the current frame if it has not been rendered). So if you have a poor GPU, the CPU may be waiting for it before telling the other box that it has finished its work.
It can get worse. Since your CPU is waiting for your GPU, you have less time than the other machine to perform the simulation. And as you must simulate every unit (not only yours, but the unit of each player), you have more work to do in less time as the game progress (as they are probably more and more unit build by each player).
In fact, in modern RTS, if you do a game with eight players and seven of them have really powerful machine and fast internet connection, but the last one has an old machine, then the game will suck for every body.