It Depends™. We recover many stolen laptops, desktops, and phones using similar methods. The problem that you'll run into is that no properly functioning unit will release information to you directly. It should only be performed as part of an official investigation as requested by an official investigative source, typically either law enforcement for local investigations or via subpoena for an external investigation.
The level of cooperation you'll receive from law enforcement will vary greatly from agency to agency depending on such conditions as technical expertise, work load, of scale of the crime committed. If local law enforcement is properly interested in working on the case, and the access of the device is geographically nearby, then you may get better results. Alternatively, if this theft is part of a string of robberies then you may similarly get more buy-in. It's worth noting that I have seen this situation be the lynchpin in finding, and bringing charges against, individuals who had performed multiple robberies in a relatively small area.
So, in short, you can't know whether the information is useful, or the device is recoverable, until after a report has been filed. In addition, this may be covered by your home owner's or rentor's insurance. The insurance company, however, won't even talk to you about a claim until you have talked to the police.