The problem with this sort of question is hat it brings in far too many modern presuppositions and expectations, the dichotomy between monotheism and polytheism is a polemic one invented by early Christians, along with the idea of true versus false gods, as opposed to native versus foreign gods. Additionally, we would need a clear idea of what reverence means.
In practice, the Greco-Roman state religion was polytheistic with a focus in participation, practical enactment of duty to the gods, rather than belief or faith in the modern sense of the word. Certainly, the state religion recognised and venerated a wide range of gods, with offering ritual and festivals.
Household and private practice along with smaller cults are widely attested in the Greek and Roman world and many of the ancient philosophers affirm belief in the existence of their gods, for instance in Plato the question of whether there is a single of any gods is not even raised - it was not a live question.
We can also examine the inscription on privately donated statues altars and votive offering to temple from common people to see that the gods were indeed recognised.
And if one examines the hymns and prayers thee are interesting ideas expressed that do not match the expectations we may have from the mythology: for instance in actual historic Greek religion the "god of X" expression is almost unheard of before Christianity arrived, and there are a number of prayers to gods, such as Ares which are quite insightful:
“I invoke Ares and Nike for the success of my expedition and I also invoke Chaerephon for if I do not invoke him he'll come without being invited.” -Apollodorus of Carystus
"Father Ares, I pray and beseech You, to be willing and propitious to me, to our household and to our family, for which I have ordered this suovitaurilia to be driven around my grain fields, my land, and my estate, in order that You may prevent, repel, and avert, seen and unseen disease, deprivation, desolation, calamities, and intemperate weather ..." -Cato
And indeed H. Versnel in Coping with the Gods says that the concept of omnipotence could essentially be held by any God, he says:
"We have seen that formulas expressing omnipotence are typical of hymns and that every god can be hailed as omnipotent in a hymn devoted to his or her divinity. " he also concludes that "Our first conclusion may be that if the Greeks should be ‘desperately alien’ they are not so in that having so many gods they must do without the notion of theological omnipotence, but in that they have so many omnipotent gods." and "This whole argument can be extended to other divine characteristics as we have quickly listed them above, especially to omnipresence and omniscience, including all-seeing."
And in Conception of God in Ancient Egypt, Erik Hornung likewise says that:
" 'Unique god, without equal': this common invocation of Egyptian gods sounds as monotheistic as anything can be. But just as almost any Egyptian god can be "greatest" ... he can also be "unique"... The apparent contradiction in logic between the epithet "unique" and the many deities to whom it is applied is easily explained. Extended and more precise forms of the epithet make clear it's true referent, which is the unique character of the divine in general. Every Egyptian gods is "unique in his fashion (wˤ ḥr ḫw.f)": there is no other who is the same as him. ..."
So it is certainly possible that someone may have been fully devoted to one particular god, but that should not be read as a collapse of polytheism as we recognise it into a monotheistic religion as we see it today, moreover, even in certain texts where we might think we see monotheism there is substantial reason to doubt such a conclusion. The ancient Greeks and Roman use of the word for "god" is particularly problematic for modern readers, since the following common issues arrise:
And in support I quote from Ger Van Riel's, Plato's Gods:
“It may have become obvious that in Plato’s texts, the gods are referred to in both the plural (θεοί) and the singular (ὁ θεός). It will be important, then, to understand this alternation, and the ideas that lie behind it, before jumping to conclusions concerning Plato’s theology…
… As the variation between plural and singular forms can thus be shown to be independent of the referents of Plato’s word θεός, one needs to look for another reason why he had no difficulties alternating between the two forms. W.K.C. Guthrie suggested that this means that the singular form has a collective meaning*. About the same time, Gilbert François conducted research into the matter in Greek literature from Homer to Plato, and came to a similar conclusion:* there is no significant difference between the plural and the singular form of ὁ θεός*, and this is not even atypical of Plato…*
... This use can be compared to that of the word ‘soul’, which may refer to ‘all that is soul’, that is***, signalling a generic description*** of ‘soul’ without for that matter denying the plurality of the various ‘souls’. In the same way, ‘god’ as a singular noun does not refer to one sole god, but rather describes all of the gods in their essential features.
Consider this example from the Republic book X: " SOCRATES: The gods have a care of anyone whose desire is to become just and to be like God. "
The translator intends us to think the lesser polytheistic gods care about people who aspire to be like the greater monotheistic God.
However, the following is just as valid of translation: "SOCRATES: The gods have a care of anyone whose desire is to become just and to be like a god. "
Here it is clear that the gods care about a mortal who tries to be like them in general, there is simply no indication of a superior monotheistic "God" other than through the machination of the translator.
So while it is possible that there were some Greeks or Roma who revered one god, there is little evidence that this was to the exclusion or denial of the existence of all others, as would be the case of modern monotheistic religion. Ultimately each case would have to be examined on its own merits.