That will depend the Slingbox model on how its connected, and the model of set-top receiver you're using.
The Slingbox is not a magical device, it can only rebroadcast what it "sees" and "hears". So, the ability on not affecting the the local viewers will dependant on the setup and configuration of the Slingbox. The easiest way to avoid a interruption is to use a video source that is not currenlty being viewed locally.
Some set-top boxes have multiple tuners with an segmented autonomous output. This is normally used to supply seperate television access to a remote location such as a bedroom or family room. If this connectivity exists and is unused, then you could connect a Slingbox to it without affecting the local viewing. However, not all set-top boxes have this feature.
The Slingbox Pro-HD also has a internal hybrid analog/digital tuner. It supports over the air ATSC and clear QAM channels. If the television provider broadcasts any channels using a compatible signal then you can use the internal tuner of the Slingbox Pro-HD without affecting the local viewing.