Okay, here we go.
In your 2600, there is a WIC (Wan Interface Card). There are different WICs for different media (ISDN, 56K, T1, T3, etc), much like there are different NICs for different topologies (Ethernet, Token Ring). Much like a NIC, a WICdoes not know your destination route. It just acts as a transmitter to send information from you router out on the T1 (much like the NIC sends data from your PC out on your CAT 5, 10BaseT network). The router passes the data to your WIC, and your WIC puts it into a format that can cross a T1. If you were changing your transmission media from T1 to a different media, you would need to buy another compatible router, or swap the WIC. You are not doing this.
Now there is the router itself. A router's job is to transmit data between two different networks. The PCs and servers on your network know that to get to your other network, send the traffic to the IP address of the router. Your router knows that it should send all traffic not destined for the local network out through the WIC. If you were to alter the subnet, i.e., the TCP/IP settings of the entire network you are relocating, you would need to adjust the TCP/IP router settings.
If you are not changing the TCP/IP settings of your networks, and are simply relocating an endpoint of the T1, there is nothing on the router to change. It is the same as if you unplugged your PC from your LAN in one room, and then moved it to another room and plugged it into the same LAN. You arestill using the same NIC card, your are still using the same transmission media, your network settings didn't change, and your destination settings didn't change. Therefore, you would not change any settings on the PC. The same goes for a router.