I wouldn't use a section of a whole branch for a neck. Lumber that contains the pith (the center of a log or branch) will always check through the pith. You could split the branch in half and try to make a neck out of it, but now you're back to a regular board, and you might as well use one from the trunk. Also, a branch that grows out sideways from the trunk will have two kinds of built-in stresses. The topside will be wood that's under tension, and the bottom side will have wood that's under compression. These don't make for very stable pieces of lumber. As was said before, you'd be best off going for a piece of quartersawn wood from the trunk or at least from a large diameter branch that's growing fairly vertical. Hickory is a tough wood with vibration absorbing qualities. That's why it's often used for axe, shovel, and hammer handles. I don't know whether this vibration absorbing quality would be good or bad for a musical instrument like the ukulele. I would think you'd want to reflect and amplify the strings vibration, not absorb it. Anyone else have any thoughts on this?
Alan