Oh yes, they did.
Probably not all Greeks of course, but enough of them.
One of the popular fads in late antiquity was Mystery Religions. These were religions that had secret belief systems that you only progressively learn as you get initiated deeper into the religion.* The gods Cybele and Dionysus had very popular mystery religions, which just flat out would not work if people didn't believe in the gods in question.
Many argue early Christianity borrowed quite a lot of elements from these mystery religions. Particularly the ritual meal, baptism, and the language in John 1 ("In the beginning was the Logos...")
The Ancient Greeks are documented to have sentenced quite a few men to death for the crime of impiety. This "crime" is not much of a social problem, unless you have large numbers of people who do believe, and are thus worried that the impiety will anger the gods, and thus cause misfortune for the community.
A lot of the early anti-Christian riots in the Roman Empire had this as at least part of the motivation. Christians denied all other gods, which would be seen as a severe danger to the community if you are a person who believes those gods exist and punish disrespect.
* - The addictive power of this scheme should be fairly obvious to anyone who understands how our own Stack Exchange network's reputation/moderation system works.