If you get taken away by paramedics after a car crash, is your car impounded?

Being transported by EMS is irrelevant. If there is evidence you are at fault and there is a potential for criminal charges or if other evidence of a crime are plainly visible, it may be impounded and held for evidence. Most times, it is just towed so it isn't a traffic hazard 

If you were injured enough to require transport by EMS, your car most likely would need towed from the scene. If you were conscious, and the vehicle wasn't needed as evidence, it is likely you would be allowed to have the vehicle towed to the shop of your choice. 

If there was evidence of criminal activity, like they found a pound of weed in the trunk, or you were suspected of being drunk at the time of the accident, then yes, it could well be impounded.  If there was no criminal activity involved, then it would probably be towed to a nearby body shop.  The last time I had an accident, I specified which body ship I wanted the car to be towed to as I new the shop was tied to my insurance carrier.   

In some areas, the cops get illegal kickbacks for towing a car to a specific body shop.  It used to happen where I live, the cop would argue with you when you requested they call a different shop. 

The police tow it if it isn't driveable, they sure aren't going to leave it the street or side of the road