Not in the same manner.
In the GDR, towns, districts and communities were assigned letters (first) followed by numbers but the letters (especially) gave no clue to the location of origin in the manner that FRG number plates did.
As such a GDR plate number "LJ 33 -45" would have the "L" designating the district of Erfurt, while the number would specify town or village more, none of this available to the general public of GDR but, of course, known to the locals.
The ministry of the Interior could, of course, look anything up in its lists.
Itzehoe has meanwhile taken the place of Bielefeld as a town that doesn't really exist.