Does Apple specify what the average lifespan of an iMac G5 would be? Based solely on the hardware used (including the power supply, logic board, RAM...) and assuming that the Software will not be updated (remain at OS X Tiger does Apple specify what a reasonable expectation for the lifespan of an iMac G5 from Mid 2005 would be? 

Does (or has) Apple provided specifications such as these for any of its products?

I am looking into purchasing one from eBay and want to know if it will last and if I can expect to receive one that is "fully functional" even after ten years.
No. Apple actually disclaims that a brand new Mac will work reliably. Only that they will repair it, replace it, or refund your purchase if you seek warranty service under the conditions of the one year warranty:


  APPLE DISCLAIMS ALL STATUTORY AND IMPLIED WARRANTIES, INCLUDING WITHOUT LIMITATION, WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE AND WARRANTIES AGAINST HIDDEN OR LATENT DEFECTS


Above from the US hardware warranty page at http://www.apple.com/legal/warranty/ for a Mac Pro

Furthermore, Apple has a long standing policy of cutting off the vast majority of repair service for Macs 5 years from the date when they remove it from sale.


https://support.apple.com/en-us/HT201624 - Vintage and obsolete products


There are some exceptions where you can get support between years 5 and 7, but after 7 years, Apple and Apple Authorized Service Centers often flat out deny repair requests due to lack of support or part availability.

I cannot find any G5 or PPC machine that isn't officially designated by Apple as obsolete in 2015.

So - in summary, a new Mac Pro isn't sold with the expectation that it will even work for one year and the expectation that it might need repairs. Certainly second hand older machines won't be vouched for by Apple to have a working life of 10 years from now. That doesn't mean some G5 will run for decades to come, just that the one you buy might or might not be the exception to things wearing out eventually.