I have a GPS auto system (laptop and Microsoft Streets and Trips).
I'm getting ready to buy a Satellite radio system.
Do I need to be concerned about any conflict between the two systems?

My guess is probably not. Different satellites, different frequencies,
different encryptions.

They will not interfere. That devices only receive data from the
satellites and do not send any information.

There should be no conflict as both devices recieve signals, not
transmit, and should be recieving at diffrent frequencies. Any
interference should be due to just haveing an operating
electromagnetic device in proximity to another - which you would have
anyway from the electrical system that is part of the engine of the
car you are going to install the equipment into - and that
interference should have a minimal impact on this equipment as it was
designed to work in such an environment.