There shouldn't be any issues with this, I've done it before using VLAN interfaces. Are you sure your DHCP server has a correct scope for this subnet so that it can assign addresses? Are you able to get a Sniffer trace on either the VLAN int or the DHCP server subnet and see exactly what packets are/aren't being sent.
What does a "show dhcprelay stat" give, does it indicate the PIX is forwarding the requests?
