Yes. Rome was a regional player with wide-ranging contacts and was noticed by the Greek world.

Eighth century tombs have unearthed objects which show Rome was in communication with other communities via trade and guest friendship ties. Status symbols such as imported ceramics and expensive metal implements show the elite, at least, had been influenced by the Greeks. Greeks had settled close to modern Naples around 770 BCE, but indirect contact with Latium was probably going on before then. Imported pottery suggest that Greek traders not only visited Rome, but had actually taken up residence there in the eighth century.

Early trade routes and communications lines in the central peninsula area have been mapped out (someone speculatively at times), which show Rome was in direct contact with nearby communities to the north, south and east such as Veii, Lavinium and Gabii. As Rome grew it became not just a way point but a main node for north-south trade.

So the Greeks probably first learned about Rome through second-hand information and then were visiting it themselves. Yet Greek authors had no reason to write about Rome (that we know of) until later.

In the fifth century two Greek writers – Hellanicus of Lesbos and Damastes of Sigeum – mentioned Rome as a foundation of Aeneas. This is actually an important point of how the Greeks viewed Rome. With Aeneas as the ultimate founder, the city and the people were placed firmly into the Greek system of how they perceived the world around them.

Here I will quote T.J. Cornell from The Beginnings of Rome:

We have no idea what Rome meant to these early writers, but it was probably little more than a name to them. Their interest, after all, was not in Rome but in Aeneas. It was only later, probably around the end of the fourth century and when the Romans first began to have political dealings with the Greeks, that Greek writers began to take serious notice of Rome for its own sake.