That really depends on which device you're using and if you have the Slingbox active. If you're not actually streaming with the Slingbox, this will not upload anything. However, if you're streaming on a mobile device or through a browser, this will stream off of the LAN and bounce back to you. Of course, if you're using the Desktop Player, either the Classic Version or the Updated Version, this will stay on your LAN so long as you are connected on your home network as well.
I hope this helps!!