Since the implementation of Positive Train Control (PTC) there is live data but the RRs don't make it publicly available. Real time GPS data is transmitted to the Computer Aided Dispatching (CAD) system and combined with consist data they can determine where any one car is located at any time.
By the time I left the company several years ago that data was being restricted to only certain employees. As noted below, hasmat is likely the reason this kind of data is not publicly accessible. It is shared in a limited fashion with shippers, etc.