I don't want to get into he said-she said, but the spectral bow most definitely has a cast time on PC (about 0.1 seconds), and is not instant cast. So technically and going by the literal meaning of the Soulshine tooltip, the set should buff the spectral bow, just like it buffs Dark Flare (another direct damage ability that has a cast time). But I would be surprised if it did.
Even if it did, it's far better to use War Maiden, which gives you almost as much spell damage but also affects all of your other magblade class skills (and comes in Arcane jewelry).