It's very difficult to answer this question with any great confidence, as the historical record simply isn't available.

The first time the eastern Greeks seem to have taken notice of the Roman state is the wars by Phyrrus in defense of the western Greek city of Tarentum. This was roughly 40 years after Alexander the Great's death.

The only Roman historian I can think of who considered the question was Livy, and he was pretty confident that the Romans would have beaten the Macedonians. As to peaceful contact between the Roman/Latin state and the Empire, he doesn't provide any information.

When Alexander the Great died, he had numerous plans in his head for the subjugation of the Western Mediterranean. It's dubious he would have given much thought to Rome and the Greek Historians point his interest as being western Sicily and Carthage. At the time, the Carthaginians and the Romans had good relations, so conflict may have been inevitable.

At Alexander's death Rome would have been little more than the formal capital of the Latin confederation. The first embassy from the successors didn't arrive until shortly after the first Punic War.

It's not a very helpful answer, I know, but it's the best answer that I think I can give. If anyone else knows something that says I'm wrong, I would love to hear it.