Yes, when the engine serial number that's in it matches the title that that was issued to the original purchaser. Lots of states, and apparently some foreign countries used the engine number for identification purposes. Lots of bolters have encountered problems with titling vehicles they purchased that had an engine swapped by the original owner, or someone down the line. Standardized "VIN Numbers" are a relatively recent thing.
It depends on whether the first DMV "title" used the Engine Serial Number (stamped into the block at the rear of the distributor) or they used the Vehicle Serial Number (on the metal plate between the hinges on the driver's door jamb).
North Carolina expects to see the Vehicle Serial Number (until a frame serial number was used around 1956). That plate must not appear to have been removed (for painting, for example).
If your Australian ID codes are similar to USA ID codes:
here are USA 1950 Engine Serial Numbers and Vehicle Serial Numbers
What are your two codes - ESN & VSN ?