Simple answer: No.
(Now for the long-winded answer)
Reason is that even if you used Firewire, your nominal speed would be 400 Mbps. Even with Firewire 800, you won't get GigE speeds so it's not practical for a company to offer this underwhelming option when people could just use the already-supplied Ethernet connector on the host. If it doesn't give you true GigE speeds, why would you buy it?
Basically, you would have to physically change the Ethernet controller on that iMac G5 and it would require some soldering expertise to get that replaced since the Ethernet controller is soldered on. You can't "force" it to do something it's not hardwired to do.
You could still use your iMac G5 on that switch and that port would transfer the data at 100 Mb. This won't slow down those hosts connecting at 1 Gb since each port on a switch is a point-to-point connection (unlike a hub which shares the nominal network bandwidth among all the ports and forces hosts to transfer at the speed of the slowest Ethernet connection). About the only thing that would slow down is data transfers between your 1 Gb hosts and that iMac, but the data transfers among the 1 Gb hosts only would be nominally at 1 Gbps (barring any latency on the network).
One more thing: though each switch port is a point-to-point connection to its end-node host, there is one caveat. If your end node from that switch port is a port on a network hub which then feeds other hosts, those hosts on the hub will end up sharing the bandwidth given to the hub by the switch's port and the speed will be determined by the slowest host on that hub.
I hope that clears things up.
As for the practicality of GigE, the only benefit is when you're transferring large data from one host to another and both ends are GigE. Having GigE will not make the internet any faster, as you're limited by how fast your internet connection to your house is. In other words, the iMac G5 connected at 100 Mbps and your GigE hosts will download data from the Internet at the same speed: 2 Mbps. This is why MisterMe said that it's really overkill to have GigE at home, unless you're doing something specialized like transferring large data among GigE hosts on your internal network.