Yes, they thought them to be real events, and were passed to them in smaller Latin forms which were well known, but still mentioned other gods.

There's a couple of ways of looking at the gods themselves though, including just placing the Christian God into the story instead. The Greeks simply encountered him, but could only use their own mythologies to explain this, so these stories became muddied. Or at least that's the sort of thinking you might encounter.

Or that they simply added in the gods because they believed them to be helping them, just as a soldier in the Middle Ages might pray to god before battle as well and find him "there" even if never literally seeing or speaking to him.

It would be a few more hundred years before people started to be a bit more skeptical of the events of the Trojan War as passed down by bards and later written down in the form we know it as (well, the two main surviving accounts of many that are now lost). But there were still people who considered them authentic accounts of a war well into the modern age, with Schliemann having been made many efforts to "prove" these stories true, to the point of fabrication or mishandling of archeological finds to try and fit the narrative into it. Today we are fairly certain that Troy existed, and we're fairly certain the site as identified by Calvert (and later more famously, by Schliemann) is indeed the true Troy, and we know that it went through many wars, including one that would match up chronologically to around when we could place such a Trojan War, but we don't believe that the details laid out in the Iliad are historical (though whoever Homer was/were he/she/they were clearly inspired by elements, including some similarly named individuals that didn't have the exact roles detailed in the book but were popular in the region that Troy was in. So there are elements there.