Yes, and what is important here is that you referred to a year by naming who ever ruled, not by a standardized year system: in the empire this had to do primarily with the ruling emperors tribun and consulship, as it had been the consuls (and probably military tribunes in the early years?) during the republic. It worked in the same way in the Greek world where they had eponym Archons (basically "giving name consul" to provide a very rought translation into Roman terms).
Here is an example of the dating, from Porta Maggiore in Rome:
Ti(berius) Claudius Drusi f(ilius) Caisar Augustus Germanicus pontif(ex) maxim(us) /
tribunicia potestate XII co(n)s(ul) V imperator XXVII pater patriae /
aquas Claudiam ex fontibus qui vocabantur Caeruleus et Curtius a milliario XXXXV /
item Anienem novam a milliario LXII sua impensa in urbem perducendas curavit
(Tiberius Claudius Caesar Augustus Germanicus, son of Drusus, Pontefix Maximus, with tribune power for the twelfth time, consul for the fifth, imperator for the twenty seventh, father of the country, undertook, on his own expense, the leading of aqua Claudius from the springs called Caeruleus and Curtus at the 45th milestone and in the same manner the leading of Anio Novus at the 62nd milestone to the city)
(My own translation)
CIL 1256 = ILS 218a, 52/53 AD.