If I Ping a Computer that is set so it won't answer Pings, Do I get anything back?

I've read about corporate servers that are set so they don't respond to Pings. But what does that mean?

To stay really stealthy they wouldn't respond at all even if they are on line. But is it more like they respond but not with a normal Ping response?

I've never run into one of these, so I have no idea, and the details seem to evade my web searches.