I asked a similar question because I was worried that if I was using the Slingbox on my local network and wanted to also surf the web on another device, that it would be slow due to the Slingbox hogging the bandwidth. What I was told is that the Slingbox is smart enough to stream over the "local" network after the initial "handshake" between the router and Slingbox. I don't know the details of how this works but that was the answer I was given. I use Comcast and use thier wireless gateway, not a separate modem and router if that makes any difference? Maybe someone else will chime in with more details.
I too hope that it is true that slinbox does stream locally when the player is connected locally, but not confirmed by support. I got slingbox 350 last week and currently access it locally as well as remotely. Even though my ISP does provide daily usage and so i am not sure how much usage is from local sling player.
One day i will try not to access from outside and locally only to find out net usage and will update.
The Slingbox 350 does stream locally when able, however Slingbox support won't really help you determine if you are correctly using the LAN. So, you're sort of on your own. I just bumped a thread where I was having an issue forcing LAN streaming.
However, you should be able to determine based on quality of the stream whether or not the data is being sent locally.