I think the answer comes in two parts:
A: If you're going to lug the machine around a lot then yes, you might need to be concerned. If it's just going to sit on your desk, probably not that much, and
B: If you take it apart to try to "fix it" (which I guess would mean either finding a non-broken iMac and stealing the correct parts, or slathering glue/epoxy all over it to reinforce it, which would look terrible) you may damage it a lot worse. (No problem if you have enough glue, I guess?)
I would swear the plastics on my B&W G3 are crumbling to bits despite the fact I haven't significantly moved or even hardly turned on the machine in three years. If you really want your example to last I might suggest a temperature-controlled and shock-mounted chamber filled with the noble gas of your choice. Anything less than that probably won't arrest the inevitable decay.