Mostly no, but to understand why we have to look at what "religiosity" meant to those cultures.

The concept of "sacred","divinity" and "holiness" were much different back then to what we (meaning the heirs of judaic-christian culture) think.In particular for the Romans something being sacred meant that it was something beyond humanity, some "other" thing that belonged to the gods. Religion, instead, meant to follow the rites that honour the gods of your forefathers and (in the case of Rome) of your homeland. What were gods though? How many were there? Where did they come from? The answer to these questions is quite hard because the gods of the various "pagan religions" (it would be better to call them polytheisms) were, as Jan Assman says, "translatable", meaning that Roman gods did not come from Greek ones, but they were two different pantheons in which each god could be "translated" or "interpreted" as the one of the other culture. Romans could not consider mount Olympus "their" holy land, because their gods did not come from there. That said, they would very much consider it a "sacred land", meaning they would show respect to the very sanctity of the place.

In their mindset, every deity was to be honored and no sacred land was to be shown disrespect, even if it was in an enemy's nation. To understand this, let's consider the concept of "evocatio": this was a rite through which ancient romans would "call out" or "summon" a city's patron deity before assaulting it in war. They did this because they considered it sacrilegious to invade and loot a sacred place. They would never have viewed anyone's sacred land as the three great monotheisms (Judaism, Christianity and Islam) do. If, let's imagine, mount Olympus fell into the hands of another empire, let's say Persia, there wouldn't have been a call to conquer it back because of religious reasons.

Many deities in roman times would be exchanged, introduced or even forgotten, in fact there was an official way to "acknowledge" a new diety into the roman pantheon, and it was done in the senate with a lot of similarities to what becoming a citizen of Rome was. In a way, every deity in the world could become a "citizen"!

In short, always keep in mind the main difference between monotheisms and polytheisms. The first worship "one true god" while the other worship "divinity" itself.

Sources:Jann Assmann - "Monotheismus und die sprache der gewalt" (Monotheisms and the language of violence)Maurizio Bettini - "Elogio del Politeismo" (An eulogy of polytheism)