Unofficial answer (but the most comprehensive answer I have found): no we cannot poison weapons. We can enchant weapons with "Cast When Strikes" poison damage, as long as you already know a poison spell. I have yet to find any mods which make poisoned weapons from Alchemy useful.
So making poisons in this game is useful only for the money gained from selling them. Poisons from alchemy cannot actually be used in combat.
This post has been edited by Renee: May 30 2018, 06:36 PM