Susan,
Based upon what I can read about the RE200, it appears to be suitable for the purpose of connecting an iMac G4 to a wireless network (that is, to use the RE200 as an "Entertainment Adapter"). The actual signal strength at the iMac G4 site is something that has to be tested. The signal strength will be affected by things like distance, building materials, interference, etc.
In principle, you could use more or less any modern wireless Ethernet bridge device (entertainment/media/gaming adapter, etc). The idea is to "convert" the Ethernet port of, for example, a computer, TV or game console to wireless (Wi-Fi), and thus access the Internet without additional cabling.
By "sharing" I assume that you mean the Internet Sharing that certain computers and operating systems can offer. A second computer would then use the Internet provided by a first computer. However, since you have a (wireless) router already, this would not be necessary. Your 2013 iMac could connect directly to the router (wirelessly, or possibly via Ethernet). When the iMac G4 is ready to be used with an Ethernet bridge, it could connect wirelessly to the router, too.