these days it would be possible, but:

a) - it has to be wired into the car to get disabled when you unlock it
b) - battery drain - you would want a separate battery for that
c) - I am not sure what you can gain with that. Even if they are stupid enough and you are lucky enough to get their faces, it is still a long shot to actually find them - unless they've committed another felony and police has records on them.

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His : 2013 X5 3.5d Deep Sea Blue/Black/Aluminum with ALL packages, 20" 214"s, running boards, Adaptive Drive, Spare Tire, BMW Apps
On Order : 2016 X3 3.5 MSport Silver/Mocha with DHP, CW, Prem, Tech, DA, Lighting

Hers : 2015 328xi MSport Silver/Red

Prior:
2008 X5 4.8
2011 X5 3.5d
2010 335 xDrive
2013 335 xDrive