Your problem is the iMac G3 does not support 802.11g Airport card or higher. That is necessary for connecting to WPA2 encrypted networks. Old WEP encrypted networks are easy to break into. So if you want any password protection, because your wireless router is less than 1500 feet/500 meters from the nearest person who my sniff into your network, you'll want an alternative WiFi connection device for the iMac G3. The iMac G3 thankfully will hook up to the LAN port of most WiFi routers, and there are also WiFi routers that have WDS distribution systems that can echo your connection to another part of the house, so you can put a WiFi ethernet bridge right at your computer if it is otherwise too far from the place in your house that brings the internet in. Not to mention 802.11b, which the iMac G3 supports with the original airport card is only 11 Mbps. And that's going to be slowest link in the chain of wireless devices on your network, making your wireless network very slow at home if there are multiple computers on it. Ethernet at least supports up 100 Mbps. 802.11n gives you up to 300 Mbps, but the improvement in speed is not noticeable on internet connections. Only when you are streaming to AppleTVs do you really start to notice the difference between 802.11g and 802.11n, and file sharing large files across your local area network.
Your Time Machine may see the iMac G3 if its file sharing is setup correctly on the same network, but you will not be able to restore the data directly to it while accessing the Time Machine from the iMac G3. The problem is the iMac G3 maxes at 10.4.11 if it has Firewire, and you need 10.5 or higher to access the Time Machine's own airport software. Older iMac G3s without Firewire only support USB, 10.3.9, and no external Mac OS X booting.