YES,
this is possible.
if you configure the port(s) of the 3560 that connect to the 2960 as a 'promiscous' port, then YES, the computers on vlan 2001 off the 2960 should be able to communicate with the 2001 computers in the 3560.
use the following commands on the 3560 interface that connects to the 2960:
switch(config-if)# switchport mode private-vlan promiscuous
switch(config-if)# switchport private-vlan mapping 'primary VLAN id'
please see the following link for more private vlan configuration info:
http://www.cisco.com/en/US/products/hw/switches/ps5528/products_configuration_guide_chapter09186a00805b57c2.html