[Zeke]

AB disclosure is common. Most understand the risks. In CA, we all allowed to paint AB and leave it in schools. What more sensitive environment is there than a school?

Painting/sealing the floor is an excellent idea. If you are going to cover the floor with carpet, why the meticulous preparation? In the long run, you might be better off doing as Janet said and just covering the existing floor. However, if you have moisture problems, that might not be the best way to go.

By "underlayment," what do you mean? Some will cover the existing floor with a vapor barrier and install sheet goods over thin sleepers. There is a lot to think about here. If you decide to shoot down any attachments whether by ram power or drilling, you are disturbing the floor. With the tile still there, this is a no-go. If you have a moisture problem, this could exacerbate it.

Aside from the original AB tile question, I'd proceed carefully.