Is it possible, with all discussed rules of Unarmed Strike/Martial Arts for it to be used with UA Mystic 3's Potent Psionics? 

>Potent Psionics
At 8th level, you gain the ability to infuse your weapon attacks with psychic energy. Once on each of your turns when you hit a creature with a weapon, you can deal an extra 1d8 psychic damage to that target. When you reach 14th level, this extra damage increases to 2d8.