Interesting question. I googled up Black Willow and found these tidbits
on forestry.about.com:
The numerous uses of the wood of this and other willows is furniture doors, millwork, barrels and boxes.
on ostermiller.org:
Light and flexible willow wood is used for wicker-work furniture and basket. It does not split when nailes. Before the discovery of plastics, toys were made from willow. Artificial limbs, packing cases and some furniture parts are also willow products. Its warm brown tones and attractive grain make it a beautiful paneling wood.
WRT using branch wood, generally, branch wood is avoided by woodworkers as the internal stress grown into the wood is released when cutting. Branch wood even after final milling can continue to release stress and distort. I suspect this would be especially true for fast growing trees, such as willow. I've had ash trunk wood "wig out" on me and bind up my TS blade as I cut it. I suspect that willow branch could be very "lively" when cut.