Not really, the marble blocks and the bronze are still in good condition, they have guided tours of the meridiana (although, as I said before, you have to go through the basement of a house in Via di Campo Marzio).
I was thinking about Roman era underground complexes (as the solarium very much used to be at the ground level) where most (or all) of the the probably few complexes are most likely to be heavily damaged or filled with mud and inaccessible. I'm having a very hard time imagining that anything like Casa dei Grifi would survive underground at the fields of Mars.