I tested it today and ended up finding a Shyvana visual bug while doing it. Anyways that aside: the results.
Does Talisman do additional damage?
Yes, when hitting the krug I got it from 1400 down to like 1357 or something the first hit and then down to like 1318 without any items (rough numbers I don't remember exact values)
Upon buying Talisman I ended up getting it the same for the first hit but during my second hit the number changed, I determined that Talisman gives roughly 2 damage per second whenever you damage a monster, but not on the second that the damage hits, it will be applied on the following second.
It's such a small number that it basically doesn't matter, but it does indeed steal hp.