It did actually. Not only in all my books (ignoring completely as well the fact that my GF was a commander of one), but online as well.
There is so much misinformation online, and records recovered in Germany after the war were confusing (i.e. total production numbers etc).
I quote:
“Simplification and standardization helped to further reduce costs and delays. The main superstructure was simplified. The side sloped armored boxes were eliminated, and the casemate sides were extended half-through the mudguard width. This extra storage allowed to store even more rounds. The engine/fighting compartment rear wall was strengthened, the ventilation fan relocated further back and appliqué armor was standardized. Furthermore, the upper MG 34 was factory-fitted, protected by a squared mask.”
and
“The main gun was unchanged, but characterized by its cast rounded topfblende pot mantlet after November 1943. Postwar, it was called “pig-head” (Saukopf or Saukopfblende). There was no coaxial mount, and the mantlet was 45 mm to 50 mm (1.77-1.97 in) thick. By June 1944, this mantlet was in short supply and the traditional trapezoid-shape mantlet reappeared alongside. In June 1944, it received a coaxial MG 34.” - The only part I have contested with this website is that some of the Saukopf pictures I have seen historically appear to have an MG ‘hole’ on the upper left of the Mantlet. And one book says some of them did fit it.
The StuG III in game right now, uses the traditional Mantlet, and is late production, so therefore, it should have its Co-axial MG34.
This is an okay online source (no source is perfect, and I’ve found discrepancies that I’ve emailed them on and have had corrected) but it is decent.