Yes. The burning of ancient marble objects during Late Antiquity and the Middle Ages was quite common throughout the Mediterranean. The marble was combusted to form mortar. I'm not a chemist and don't know the specifics, except that the marble was destroyed in a kiln and mortar was the result. It was such a vast industry in Rome that the district where the kils were concentrated came to be called the calacario, "mortar district." The ancient Roman Mediterranean was positively covered in marble: statuary was a fixture of every Roman city; flooring; decorative cladding on the walls of buildings; columns (either solid marble or with marble cladding; etc).

Rome is a special case because there was just so much marble there. The vast Baths of Caracalla alone had enough marble to keep the kilns burning for decades, maybe centuries. In other places, Athens included, the physical evidence for the kilns is not as obvious. They were often ephemeral emplacements, located very near the source of the marble and then destroyed when the source dried up. That makes finding them in the archaeological record difficult. Still, we have a number of very good examples of the kilns themselves and the archaeology around how the operations worked. One great example is at Butrint, where we can see a very clear overview of the evolution of the Roman forum there from public space to kiln feeder. Another great example of lime kilns is at Ostia Antica, the old port of Rome. This was a sort of clearinghouse for burning marble which had been hauled out of the ruins.

One might wonder why a medieval person would burn a lovely statue of Venus in order to get half a wheelbarrow of mortar. The simple answer is that an Italian peasant in 950 CE did not care about Venus, nor really about statues; what he did care about was building or repairing the buildings of his own time, especially churches, and tossing marble in the kiln was the cheapest and easiest method for obtaining mortar.