There was a Graeco-Buddhist culture in Bactria, centred on Gandhara, during the 4th century BCE and 5th century CE period. Also, there were Sramana Vedics such as Zarmanochegas, so why not Buddhism? There was a Lakshmi statue in Pompeii. From my understanding, with trade between Bactria, India and China during the Roman Empire it's unthinkable that there wouldn't be some spread of Buddhism into the Roman empire.

So, it's entirely possible there were Buddhists prior to the Middle Ages, especially during the Alexandrian and Roman Empires - where there was significant trade in Bactria and India to Europe. However, due to competition from the official state religion of Rome, and later Christianity, it's highly unlikely a large body of Graeco-Buddhist or Romano-Buddhist writings have survived, due to what I interpret to be a scarcity combined with the tendency of any mystery cults in Rome to be secretive, makes it hard to quantify.

Whether or not they influenced Christianity, Judaism, Islam I'm unqualified to definitively say. However, I doubt it was anything significant due to Christianity's significant deviations from Buddhist theology and morality, and because Islam is very iconoclastic, and historically Islam did not treat Hindus and Buddhists with much respect. However, if syncreted religions during the Roman Empire interest you, definitely read into Mystery Cults such as Mithras and Isis worshipping ones.

Sources

Huff ML. Civil Disobedience and Unrest in Augustan Athens Hesperia 1989

Foltz, Religions of the Silk Road

Mahavamsa, Chapter XII: https://web.archive.org/web/20141020052522/http://lakdiva.org/mahavamsa/chap012.html

Lakshmi Statue Articles: http://www.pompeiin.com/en/Lakshmi.html, http://www.sanskritimagazine.com/history/ancient-pompeiis-lakshmi-statuette/