Earlier Novars did carry a serial number. I've yet to see a postwar Novar with a serial number.
In any case, you can sometimes tell if you have a very early camera by the shape of the camera. The earliest Ikomat/Ikonta cameras had sharp chiseled edges, while the later models had more rounded edges.
The Novar was the budget lens, while the Tessar was the premium lens.
Even so, stopped down, the Novar is a very capable lens.
For the most part, Zeiss Ikon didn't make cheaper cameras. The lens was always the factor in determining price. That changed in the 1960s and 1970s.