Ship Wreck,
Yes you can install tile on cork without a backer board. The important thing is to make sure you use the proper adhesive on the sub floor to cork.
Here are some information from our website.
SETTING CERAMIC TILES
Use any of the following products to install ceramic tiles...
Linoleum will be much cheaper and very durable if you are worried about money.
You could go the cork route but you should use glue down tiles instead of a floating floor. Make sure you caulk around the perimeter and put 2 coats of polyurethane to seal the surface for good measure
John...
I am assuming you have a apartment above you and you want to muffle the noise you hear from above. We have had customers order underlayment and stick it to the ceiling but I have never heard back from them on how successful this is. The best method which probably isn't practical is to insulate...