Yes, it does, but you really should stop using AppleWorks. It will break eventually, and you don't want to be stuck with all your documents in AppleWorks format when it does.
I installed Snow Leopard and AppleWorks gives me the Beachball of Death more than ever before. If AppleWorks is vital to you... either stay away form Snow Leopard or prepare a plan to downgrade back to Leopard should you choose to find out for yourself how well AppleWorks runs in Snow Leopard.
EDIT: I re-installed AppleWorks and it seems to work better than it did in the previous install (since upgrading to Snow Leopard).
Appleworks has to be the latest update 6.2.9 .
On my new MBair snow leopard 10.6.1 it works a bout X times faster than on my powerbook and without any problem at all.