Do you think the images of our ancestors still reverberate today with meaning and insight?

Viewing the work of one’s ancestors is like opening an diary. The imagery is a snapshot, capturing a vision of the period from the perspective of the artist that— coupled with some reading for cultural context— gives an intimate view of the times. 
The work is like a memory. In the same way one might recall a mistake or a great success and learn from it, one may also look to how the piece deals with its subject matter and pull out lessons. We can glimpse the way a society views its predecessors or principles too by comparing depictions of the same events across cultures and time. Caravaggio shows Saul’s experience of God differently than an artist might have before him, creating an intense air of drama around little more than a shock of light, which compared to the past use of hands descending from the clouds and glorious angels suggests a different way of thinking. By viewing work like this  one can pick up on the ideas that compelled the people of the times and, perhaps, understand how today’s society has been shaped as a result.

Your first step in answering this is to examine the underlying assumption of the question. An image does not just "reverberate" on its own in the absence of an audience. A response to a work of art is always the response of an individual interacting with that work. Since there are some 7 billion people alive on earth now, one cannot possibly know how each of those billions of people might interact with every single work of art created before they were born. 
If one looks at statistics of how many people visit museums or monuments to view the "old masters" it is obvious that some people find these works of interest. People stand in line for hours to view the Mona Lisa in the Louvre and tourists flock to sites such as the Athenian Acropolis, Knossos, or Pompeii. Although some people may find contemporary art more accessible or interesting, many others find older works more inspirational. 
Personally, I would suggest that viewing only the work of one's contemporaries is just as narrow-minded as never leaving a single small town and never meeting someone from a different ethnicity, social class, or religious background. Images from a distant period in time are inspiring precisely because they force us to think and respond outside the circumscribed temporal nature of our own lives.