You can test this without a network, just by copying from c:\temp to \\localhost\c$\ or something.
That's why the CPU is so high on my test. If you remember from the OP, an actual network transfer only spikes the CPU to around 60-80% w/ Avast, and only 15% or so w/o.
However, taking the network bottleneck out of the equation and just copying from a local drive to localhost, it uses the network layer, but doesn't actually go out on the network. This makes the test easier to do and exacerbates the problem so it is more readily visible.
I'm thinking that Avast! is simply hooking into the server process, and even though the network shield is disabled, the hook is still there, and executing some bit of (inefficient) code in Avast! that appears under the System process.
I should also note that the CPU spike ONLY happens on the destination, not the source. (so copying from \\localhost\c$ to c:\temp would NOT reproduce the issue.)