Absolutely not. I'm not a classicist, but I do have an interest in the ancient world. One of my favorite professors when I was an undergrad was a classicist, and his argument for why Athens even became so intellectually inclined and "progressive" was because they had slaves do everything. Athens, by far, had the most amount of slaves of any city-state. I would say it wasn't a "utopia" for that reason alone.

Moses Finley in Economy and Society in Ancient Greece puts the number of slaves at about 80,000 in the fifth and sixth centuries BC. That's 4 slaves per household. Couple that with the fact only men born in Athens had any rights, I wouldn't exactly call it a "utopia." That is, unless, your definition of utopian democracy grants no rights to women and children and is built on the backs of slaves.