Hi, the short answer is yes. There are many instances of significant political contact between the Romans and Greeks prior to the Roman conquest of Greece. An important thing to remember is that the Greeks colonised regions outside of Greece, for example in Sicily the Greek city state of Syracuse had significant contact with the Romans and played a role in the Punic Wars (sided with Carthage) (for reference the first punic war occurred between 264-241BC).

Whilst not technically Greek, the Romans also had significant contact with the Macedonians, notably in the first Macedonian War (214-205BC) which was fought concurrent with the Second Punic War that came about due to the Carthage-Macedon alliance that was forged.

Another major example of this contact is the Pyrrhic War, by which Pyrrhus from the Greek city of Epirus invaded the Italian peninsular in an attempt to annex it to his control. It is this war which led to the coining of the term “a pyrrhic victory” , due to Pyrrhus actually having won all his battles, yet losing the war.

These are just some major examples I can think of though there are surely more, likely pertaining to trade as Rome would have had contact with other Greek colonies (for example: Neopolis "Toynbee, Hannibal's Legacy pp136").