No, you cannot reliably root a palm plant in water.
Based on available information, attempting to propagate palm trees through water propagation is generally unsuccessful. The provided reference clearly states it "does not work" and is a "failed attempt." Palm trees are not known to readily root from cuttings in water. The video also mentions attempting soil propagation as an alternative, implying water propagation is not a viable method.
Therefore, if you are looking to propagate a palm tree, water propagation is likely not the answer.