Can one write on those new Windows 8 touchscreen ultrabooks with a stylus?

TL;DR: While you can write using a stylus, there are tradeoffs, and it's generally not worth the trouble.

These touchscreen Ultrabooks have capacitive touchscreens, so if you wanted to, you could get an iPad stylus, like this one, and use it on the touchscreen.

However, because they don't have active digitizers, they cannot get the resolution that conventional Tablet PCs have. As a result, you have to write much bigger and more deliberately than you would with, say, pen and paper or a tablet with an active digitizer.

It depends on the ultrabook.

Some might only have the touch screen. And as was mentioned, you can use a capacitive touch stylus to do some writing on the screen, like how people take notes on their iPads. However, this is inferior to using a digitizer stylus, which support pressure sensitive writing, higher sensitivity, better palm rejection, hovering, and support for stylus buttons (for things like eraser mode and right-clicking).

Some ultrabooks and tablets do have digitizer stylus support. I don't have a complete list, but I do have a Sony VAIO Duo 11, a convertible tablet/ultrabook with a digitizer stylus. I believe the Lenovo Twist, Samsung ATIV Smart Pc Pro, HP Elitepad, and Microsoft Surface Pro all have digitizer stylus support.

These devices would work very well with OneNote. In fact, that is what I use mine for at work.