well lets look at what you have vs what you need.

Mac mini .. outputting video through DVI (or VGA adapter). and you have an old G3 iMac, with no video input.

short answer: no.
even though you could probably feed the video in with firewire through an input device, or take apart the iMac housing and adapt the input for VGA. but that would probably be more work than spending $50 for a 15" CRT.