Hmmm...well it is possible, as the others have said, but it seems like a lot of work for this particular design.
The designer seems to be using a cut and tie off method, but that's time consuming, though it would save you the trouble of getting your skeins/bobbins of yarn all tangled up. All those yarn ends on the inside would add to the thickness of the scarf though.
You could knit the entire thing flat, and seam up the side.
If it were me, though, I'd knit it flat with traditional intarsia, but only one "side" of the scarf. Then I'd line the back with a nice thin coordinating flannel material to cover the back side of your work.