Yo! So in the future I'd ask these sorts of questions in /r/linguistics since historians don't tend to be experts on historical languages or linguistics. I'm not an expert either (just a linguistics undergrad with an interest in this sort of thing) but I figure I'll respond to the best of my knowledge.

So, basically, the answer is no... sort of. In reality it's more complicated than that. Latin is, as with the majority of the languages of Europe, an Indo European language. This means that it descends from Proto Indo European (henceforth PIE), a hypothetical ancestor language that has been largely reconstructed, which was probably spoken in central asia some time around 4,000 BCE.

Some time around then, the Indo Europeans (IEs) began spreading out in all directions, and their language began to split into different dialects. Those dialects eventually became the primary IE branches, which then split into more languages and so on. Those primary branches are from west to east:

Celtic, Germanic, Italic, Slavic, Greek, Albanian, Armenian, Anatolian (extinct), Indo-Iranian, Tocharian (extinct) and possibly some others we don't know about. Here's a map, although it doesn't quite show what I'm describing - in many cases it shows where these sub families are spoken today rather than where they used to be spoken.

Latin is part of the Italic sub family. It had many Italic sister languages - Faliscan, Umbrian, Oscan, etc. although none have survived to the present. When Rome spread and conquered the entire Italic peninsula, speakers generally transitioned over a few generations to speaking Latin. This is why today we often refer to the Italic subfamily as the "romance" family, as the only living languages that belong to it are romance languages, descendants of Latin.

Interestingly, Etruscan was almost certainly not an Indo European language, and was completely unrelated to the Italic languages. Etruscan was one of the few pre-Indo European languages of Europe to survive into antiquity. Today, only one pre-indo european language survives in Europe, that being basque. All others were either replaced by Indo European, or came along later (like Hungarian and Finnish).

Just for fun, here's a phrase in Faliscan, Latin's closest sister language, and then in Latin:

Faliscan:

Foied vino pipafo, cra carefo.

Latin:

Hodie vinum bibam, cras carebo

English

Today I will drink wine, tomorrow I won't

Literally:

Today wine I will drink, tomorrow I will lack

So, Latin fits in just fine with its Italic sisters, is unrelated to Etruscan, and is more distantly related to other IE languages like those spoken by the Germanic tribes, the Celts, the Greeks, etc.

So, with that out of the way, what about Troy? Well, Troy is believed to have been a costal Anatolian city - modern day Turkey. As I mentioned before, Anatolian was one of the ancient branches of Indo European. Fascinatingly, the first/most archaic Indo European language to be written down was Hittite in the 17th century BCE, and it was an Anatolian language. The last Anatolian languages had all died out by the 5th century CE, by which time pretty much everyone had switched to Greek. Troy probably existed around the 12th century BCE, and in that time and place they probably spoke Luwian a fairly close relative of Hittite.

So, the language of Troy, if it really was Luwian, would have been related to Greek and to Latin, but they all belonged to separate branches of Indo European.