No, it is highly unlikely. From the 5th century B.C.E. to 338 B.C.E., Rome was part of the "Latin League", a confederation of politically sovereign villages/cities located in what would eventually become known as the province of Latium, in the midwest of the Italian Peninsula. The participants, although politcally autonomous, were linked together through their worship of common deities (Venus, Jupiter) as well as belonging to a broader, Latin linguistic group. The organization primarily served as a mutual defence pact, through which the inhabitants of Latium would come together to defend the region from Etruscan aggression via an interconnected system of hill forts and manned outposts. Rome possessed some territory surrounding their city; they were a fledgling city-state steadily increasing their influence within their immediate environs, but were by no means an empire. Tension within the Latin League fractured it, and Rome found itself warring against formerly friendly Latin cities. This resulted in the dissolution of the Latin League in 338, and Rome, emerging victorious, annexed several cities. Thus, when Alexander died in Babylon, in 323 B.C.E., his empire stretched from Macedonia and Egypt to the Indus River Valley in modern India, whilst Roman imperial ambitions were in their nascent stage. They possessed a handful of villages, cities, and military outposts, but were not yet a major power by any means. It is likely that Rome at this period was known to the Greek world via commercial trade routes, but was Alexander aware of their growing influence in a small part of Western Italy? Probably not. Logistical difficulties aside (Alexander was half a world away), Rome was just not a major player in the Mediterranean at that point.