Yes, iMac G4s rated 1.0ghz or higher had a slot for an Airport Extreme card. If you put in an Airport Extreme you will be able to connect to the 802.11g network provided by the Linksys router.
Earlier iMac G4s (less than 1.0ghz) only had a slot for an original Airport card, though, which would not be a desirable option. If this is the case for you, I'd recommend buying a third-party USB 802.11g adapter.
- iMac G5 1.8GHZ 17" | SuperDrive | 160GB | 512MB | Airport Extreme | Bluetooth Keyboard & Mouse | Wacom Intuos II
- Pentax *ist DL - JVC MiniDV Camcorder - Airport Express - iPod Nano 1gb white