The answer is: maybe! Thucydides (6.88.6) reports that Athenian envoys sailed to Carthage in 414 B.C. seeking aid during the Sicilian Expedition, though he himself claims elsewhere that some Athenians (i.e. Alcibiades) hoped to conquer Carthage in the future. [1] An actual alliance might have come about in early 406; evidence for this comes from a very fragmentary inscription (discovered in Athens in 1939 and reconstructed by Benjamin Merritt in 1940) bearing some sort of honorary decree to the Carthaginian generals Hannibas and Himilkon. As we know from the historian Diodorus of Sicily, Hannibas and Himilkon were leading a military campaign in Sicily at the time. We can extrapolate little more from the inscription, unfortunately, because it is so badly damaged. Merritt, noting that "much in the inscription is ambiguous," concluded that "what seems certain is that a mission was sent from Athens in 406 B.C. to consult with the Carthaginian generals..." [2]

As a bit of trivia, the same Carthaginians actually appear in a Punic inscription describing the attack on Akragas/Agrigentum later that year. The text was first deciphered by C. R. Krahmalkov in 1974, and I adapt his latest reading below (though it has some issues, these probably won't concern anyone who doesn't read Phoenician-Punic): "...and the rbm Adnibal son of Gersakun the rb and Himikot son of Hanno the rb marched at dawn, and they seized Agrigant (=Akragas), and they (=the inhabitants) made peace, including those who had fled..." (wylk rbm ’dnb‘l bn grskn hrb wḥmlkt bn ḥn’ hrb ‘lš wtmk hmt ‘yt ’grgnt wšt [hm]t šlm db b‘l nws) The title rb just means "chief," but here it probably just denotes "general."

I hope this helps! :)

[1] See also Max Treu, "Athen und Karthago und die thukydideische Darstellung," Historia: Zeitschrift für Alte Geschichte 3 (1954), 41-57.

[2] Benjamin D. Merritt, "Athens and Carthage," in Athenian studies presented to William Scott Ferguson (Cambridge, MA: Harvard University Press, 1940), 247-253. The text also appears in Russell Meiggs and David Lewis, A Selection of Greek Historical Inscriptions to the End of the Fifth Century B.C. (Oxford: Clarendon Press, 1969), no. 92.

[3] C. Krahmalkov, "A Carthaginian Report of the Battle of Agrigentum," Rivista di Studi Fenici 2.2 (1974), 171-7. Defended and discussed at length in Philip C. Schmitz's dissertation "Epigraphic Contributions to a History of Carthage in the Fifth Century B.C.E." (University of Michigan, 1990). Krahmalkov's most recent reading can be found throughout A Phoenician-Punic Grammar (Leiden, Boston, Köln: Brill, 2001).