You very well might be correct as the Roman coins I have seen were largely illegible.
I was basing my guess on the dates I have seen on early Roman writings, which used either or both the AUC or the years of the Consuls serving at that time,
The historians usually use the consuls’ names if they bother to date at all (I just glanced at Eutropius, a 4th-century A.D. historian, and he doesn’t seem to date events at all.) The standard dating of the founding of Rome in what we call 753 B.C. is by Varro in the 1st century B.C., but it doesn’t seem to have been used in daily life.