I just tested it with an ebony axe with a shock (20 effect) enchantment, with and with out a 30% weakness to magic potion. Against the same opponent it took 18 swings without the poison and 15 or 16 swings with it. I tested it several times with the same results. I was doing around 42 points of damage with the axe with no poison, and around 48 with it. So the poison seems to work with enchanted weapons.
(it takes a 100 alchemy skill with alchemist 5/5 and poisoner perks (no items or other boosts to alchemy) to make that strength of poison - seems like a lot just for a few less swings - perks that could be used to increase the base weapon damage instead)