I don't think it will happen, but here's something to ponder:
When Honda started Acura way back when, a lot of people said it wouldn't last. How many people are going to pay extra for a dolled up Civic? 20 years later, the answer is, "plenty". Nissan and Toyota got the hint as well...
Not everyone can afford an Acura though, so they buy a Honda now because of its perceived reliability, love it, and make the switch to the "luxury" version when their income justifies it. Could something similar work in the computer world?
If Apple were to license their "engine" to non-Apple manufacturers, how many people would buy into it? Even if the hardware options were limited to a very, very short list and Apple got a percentage of every one sold in addition to the cost of the OS, PC manufacturers aren't going to complain knowing how fast OS X is growing in popularity (not to mention other Apple branded hardware and software); they'll still have good profit margins and the revenue potential is huge. Even if we're talking a couple hundred bucks difference, the market is there. And DIYers would definitely see the savings potential.
Would it be as pretty as a Mac? Probably not. Would it be as good as a Mac? If Apple holds onto a few key luxury technologies, such as Touch, it will be close, but not quite. Would people who want Apple but can't afford a MBP while going to college look forward to the day they are making more money and would thus willingly pay more for the prestige computer? More than most people would think, I'll bet.
Has everyone forgot about the lack of updates to the perpetually doomed Mini - the "low-priced" BYOKM computer that was supposed to hook Windows users? How long have people been waiting for a mid-tower? Alleged lack of updates to the Mac Pro aside, is it the hardware or the software that makes it such a desirable product for professionals?
Steve Jobs has not been shy about predicting where computing is heading (with Apple leading, of course) - mobility. Desktops and servers are not dead or dying, but laptop sales will overtake desktop sales very, very soon. And the forefront of technology is the ultra-mobile concept; the iPhone and iPod Touch are just the beginning of where Apple is likely to go.
Remember the uproars when Apple dropped "essential" items from their lineups? How can we live without a floppy drive? But I love my s-video out! Apple could one day drop all desktops to a jaw-dropped audience, and all Jobs would have to say is, "who really needs them?" and 90% would wake up and say, "good point". The other 10% still have OS X equipped options.