If you're able to build a static one-to-one address translation on the LinkSys that maps to teh 2600 then yes, this should work fine, just point the peer address on the PIX to the NAT'd address in the LinkSys.
If the 2600 is on a private network behind the LinkSys and the LinkSys only does PAT, then no, it won't work and you'll have to put the 2600 in parallel and give it a valid routable address.