I'd rather suggest adding a bridge (possibly anonymous = sans IP address), in other words turn the Pi into a 2-port ethernet switch, that will see all the traffic pass through it without changing anything to the network setup.
- Install on the Pi the software packages you want to use,
- Add an USB adapter to the Pi,
- Create a bridge br0 with both eth0 and usb0 in it,
- Disconnect everything from the router except WAN and one LAN cable,
- Stick the LAN cable in the Pi,
- Connect another cable from the USB adapter to a switch on which LAN clients are connected.
So for this recipe you need: 1 gigabit USB adapter, 1 ethernet switch, 1 ethernet cable, Pi and accessories.
If you need to see wifi traffic as well, altering the router, and possibly clients configs will be required:
- Disable the AP in the router,
- Create one with possibly identical parameters in the Pi,
- Add wlan0 to the bridge.
Ethernet or wifi, performance will suffer so the setup is not going to be as "transparent" as it can be.