Of course you can hear sounds: but you can only hear direct sounds. All reflected sounds are gone. And that's actually a high percentage of the sounds you normally hear.
An anechoic chamber is used to test acoustics in an environment with absolutely no reflection (reverb, echo, etc.).
You got to try an anechoic chamber to believe it. BTW: many universities have one. The one I worked at (BYU, long ago) has this one:
http://www.physics.byu.edu/research/acoustics/facilities.asp...
http://vimeo.com/15855229 (a corny advertisement, but shows the room well)
http://www.youtube.com/watch?v=0PGF_cGS8ts
It's a very good facility. Interestingly, I believe the main anechoic chamber used to be an echo chamber!