Obviously it would “technically possible” to run X86 applications on ARM-based machines, but that would at the very least involve emulating an Intel CPU on an ARM one, but the ARM-based machines may already have their hands full running huge Windows applications like Outlook without any emulation, so you can only imagine what would happen if every single machine-code instruction had to be emulated… This just sounds like a terrible idea.
But it may not be as bad as it sounds. Most Windows Apps can be recompiled and tested and that would involve only a tiny fraction of work when compared to porting the app for a different environment. Most applications are very abstract from the processor anyway. The question is: will app developers take the time to do it?
My guess is that a lot of them will, if the Windows+ARM platform is getting a minimal traction. Microsoft has demonstrated Office running natively on ARM processors, and although Office is not the sexy talk in town, a huge number of users still count on it on a daily basis.