Yes, but how well will these parts interoperate. That's always been a major problem with these cobbled together PCs, it's exceedingly difficult to know if driver issues and other problems that, IMHO, can eat you alive regardless of how good the individual parts are.
I think Apple could create a headless iMac without affecting their product line much, but it would never compete with the prices a "custom" model would have.
the stuff you're describing happened in the days before plug-and-play was mature...as in the early to mid 90s.
in this decade, as long as you buy a decent piece of hardware from a reputable manufacturer, and you don't buy the wrong type of RAM or a graphics card with the wrong interface slot, you won't have any issues at all. "these" PCs arent' "cobbled together" at all. You have a case. It has a power supply in it. both of those are almost always ATX-compatible, which means they work together. You get a motherboard for either AMD or Intel and for the processor family you want (Core, Pentium 4, Athlon 64, or whatever). It will also be ATX, and will thus fit into your case and work with the power supply.
You get a processor and plug it in, and put a heat sink on top, which probably came with the processor.
you stick in the RAM in the RAM slots.
You put in the optical drives and connect the cables. Hard drives, too.
Attach any fans or whatever else you might want. Then you plug the motherboard into the power supply.
Add any sound cards or graphics cards by undoing at most 1 screw and plugging them into the obvious slots.
close the case, plug everything in.
turn on the power.
insert install DVD and install the OS. If vista, then when it reboots, it will have gone to windows update and pulled down certified drivers for graphics, audio, etc, and everything will be up and running if you bought good components.
After the first time you do this, it will literally take longer to let the OS install itself from the DVD than it does to put everything together physically from scratch.
It isn't some big mythical, fragile, confusing system. There are many more variables involved when you go to the grocery store, but people seem to manage that just fine without complaining about how "cobbled together" their shopping carts are.
If I could easily build a PC with complete support for OS X from Apple (not actual tech support, but rather just "permission"), I would never buy another Mac machine. I'm not driven very strongly by my ego and what others think about me. I don't need my computer to be shiny and coated in glass and all of that junk. I would prefer it be hidden out of the way except for the screen and the kb/mouse, but a plain black box is fine. I guess that's why Apple isn't ever going to open up OS X. They know people would stop using their hardware. Well, serious people would, anyway.
To argue that apple uses superior hardware is increasingly difficult. With a mac pro, the case is high-quality. The fans are low-noise. The required RAM is server grade (and thus unnecessarily expensive) but everything else is off-the shelf.
If you value the mac pro's case at about 300 dollars and the PSU at about 150 dollars, then pretend you can put non-server parts into it and thus get the same performance for considerably less, you end up with a HUGE premium to pay for them to plug some cards into some slots and screw a few things together. It's a bummer.