Not according to Michael Foley, who teaches Patristics at Baylor University. Here's what he says:

'Another widespread myth is that the early Church had Mass “in the vernacular.” But when Jesus worshipped in the synagogue, the language used was Hebrew, which had already been dead for 300 years. And for the first three centuries in Rome, the Mass was mostly celebrated in Greek, not Latin, which was only understood by a minority of the congregation.'

NB: when it was offered in Greek, that "was only understood by a minority of the congregation."

He adds: "Moreover, the Latin used in translating was deliberately different from what was being spoken at the time: It had curious grammatical usages and was peppered with archaisms." It was a "hieratic" form of Latin, not the common tongue. See: http://www.crisismagazine.com/2011/five-myths-about-worship-in-the-early-church.