There is known dates for when zimmerit was applied at factories. Basically from December 1943 to early September 1944. The Stug IV began production during this time frame, so if you are building your model of a vehicle in action during this period, then the answer is easy - it should have zimmerit.
There is a pdf list here of the allocation of Stug IV, beginning page 14.
http://missinglinks2.tripod.com/stugiv.pdf
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There is some question of the Stugs with Lehr during Normandy. A book I have states ten vehicles were given to the third company of Panzerjäger-Lehr-Abteilung 130, which had not yet received its Jagdpanzer IV's. Wiki entry has it at only nine vehicle's, replacements in lieu of five Tiger II that never joined the unit due to breakdowns.
https://en.wikipedia.org/wiki/Panzer_Lehr_Division#cite_note-16
regards,
Jack