Yes, of course. Phoenicians were the Persian Empire's main naval force, aside from the Greeks of Asia Minor, and the Greeks of Sicily and Carthage were on-again-off-again for a couple hundred years, until Rome showed up. There is some suspicion that Carthage was cooperating with Persia during the 480 invasion to prevent the Greeks of Sicily from helping the Greeks of the homeland. The way Herodotus tells the story, Gelon, the tyrant of Syracuse, refused to help the Spartan and Greek ambassadors against Xerxes when they refused to give him supreme command. But Gelon fought off a major Carthaginian invasion at Himera the same year, and it's entirely possible Gelon chose not to participate in the mainland campaign to fend off the Carthaginian advance.

The combined Greek navy knocked out a Phoenician fleet at Mycale in 479, and about a decade later the Delian league scored a major victory over a Phoenician navy at the battle of the Eurymedon.

The possibility of a Phoenician fleet present in the Aegean remained a point of concern for Athens. I'm weak on my Greek oratory, but doesn't Demosthenes mention this possibility in a couple of his naval speeches?

So yeah, Phoenicians were a concern for Greeks both in the East and West.

Someone already mentioned the role the Phoenicians played in the Persian Wars. There's also a fair bit of drama between the Greeks and Phoenicians as they expanded into the Western Mediterranean. Thucydides and Herodotus both mention the Carthaginians --and in the case of the Battle of Alalia a Carthaginian-Etruscan alliance-- engaging in a number of sea battles with the Phocaean colonists who were establishing the new city of Massalia (modern Marseilles).