That's a great question! The answer really depends on the capability of your specific DVR/ cable or satellite box. I personally have a Slingbox connected to a secondary receiver (non-DVR) at home which has access to my main receivers DVR functions and I am able to access recorded shows without interfering with the main DVR. When I am streaming via SlingPlayer, it will interfere or "take over" the secondary receiver but will not interfere with anyone at home watching TV on the main receiver or watching another recorded show on the main receiver.
I would advise either contacting your provider to determine the functionality/ capability of your "whole home DVR" experience, or just test it our yourself. If you are able to access recorded shows from the secondary receiver without interfering with the main receiver/DVR at home, than you should also be able to stream via the Slingbox with the same result.
Hope this helps!
The Sling Moderation Team