If you plugged the outside interface into your LAN and you have DHCP enabled on your LAN, yes, it should pull an IP from DHCP and should be able to access the Internet.
Does the concentrator actually respond to pings from the Internet? I would try to ping it from something else, and try to ping something else from the PIX. Not responding to ping doesn't necessarily mean the VPN won't work.
Without knowing how the concentrator and PIX are setup it's hard to say, but keep in mind NAT could be a problem. You may need a public IP on the PIX, or to change the configuration of one or both sides so it works with NAT between.
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