Yes and no, at least in the early middle ages.

In fact, preventing written Latin from "evolving" was a major concern for scholars of the Carolingian Renaissance. In the Merovingian period, Latin spelling had changed to reflect changes in the spoken language.

Carolingian scholars sought to restore Latin spelling to what Alcuin of York, who wrote a text called De Orthographia, called the "Roman sound". (One preface to De Orthographia reads 'me legat antiquat vult qui proferre loquelas': 'let he who wants to speak ancient words read me'.)

It's noteworthy that Alcuin (and several other scholars at Charlemagne's court) were from the British Isles, where spoken Latin and its descendants had long died out. Perhaps the idea of Latin as a pure language to be rediscovered was more obvious to them.

Sources: The Making of Textual Culture: 'Grammatica' and Literary Theory 350-1100, Irvine M (2006)

Carolingians and the Written Word, McKitterick R (1989)