Specifically, around the time Spanish explorers began landing in the New World.
Yes, they occupied the coastal and northern areas. Since they were still city-states they proved to be difficult to conquest by the Spanish. In fact the last Maya kingdom to fall, Nojpeten, fell in 1697 due to the efforts of a young man trying to regain some of the glory of his family of conquistadors. The Maya Collapse is a misnomer because it was more of an abandonment of a particular region and a change in their sociopolitical structure.
Grant Jones - Conquest of the Last Maya Kingdom (1998)