If I understand correctly, the Extreme Base Station (AEBS) is the router for all, and there is a switch connected to the LAN (local) port to increase the number of ethernet ports. You want to attach the all-in-one to the AEBS USB port to share it? Only the printer will be usable that way. Read the 2nd paragraph:
On the other hand, if you connect the AIO to one of the computers, you can share it (all functions) with all the others.