I understand that you would like to know if you will be using your broadband connection when the Slingbox is streaming.
Please note, that in case you are trying to connect from a remote location, you will be using upload/download speed. Also, as per the minimum requirements, the upload should be 3M for you to get HD signal.
You can check the following link about it.
Since Slingbox sends the audio and video over the Internet, then I certainly think that it is true that your ISP will record the data entering your home from your brother's Slingbox, just like any other files that you might download. Ten gigabytes per month seems to be a rather paltry amount -- my ISP in Colorado limits the monthly transfer from a "regular" home account to 250 gigabytes per month. I have never come close to that limit -- I would probably have to be streaming video from my Colorado Slingbox to my computer outside that home for nearly 8 hours per day to approach that 250 gigabyte limit.