The short answer is yes.

Archaeologists routinely find Postclassic ritual pottery (mostly incense burners) on the surface of Classic and Preclassic buildings, indicating that people went there specifically to conduct rituals. Lacandon Maya still use ancient buildings for rituals directed at ancestors. There are also plenty of places, especially in the northern lowlands, that have been continuously occupied since 500 or 1000 BC, so nobody ever forgot. Yaxuna is a good example.

There are also numerous ethnonyms (group names) and family names that are clear relics of the Classic period that pop up during the Postclassic. These may be about as direct a connection as Kaiser and Czar are to Caeser, but they indicate a thread of continuity and memory nonetheless: Ah Canul, Itza, etc.

There are numerous place names that continued on from the Classic period into the Colonial era and some right down to the present day. Examples include Yaxha in Guatemala and Ek Balam and Tiho in Yucatan (the latter is what became Merida after the Spanish razed it). Although toponyms are notoriously "sticky" and the fact that they endure doesn't say much about cultural memory. Tons of indigenous place names in the US but most Americans couldn't tell you squat about the people who gave them those names.

However, by the 20th Century most of this memory had been lost. There is a famous folktale that explains the pyramids and the maize grinding stones that occur nearby with reference to an ancient quasi-human group of miniature people who lived when rocks could float. They built the pyramids with little effort because rocks were so lightweight. But Chaak decided to get rid of them, sent a flood, and they tried to ride it out in their stone canoes. So Chaak made stone heavy, the canoes all sank, and that's why there are so many hollowed-out big rocks around pyramids. One of my favorite just-so stories.