Ok, I'm confused. Let's work this out. Jen the Nosferatu wants to bring that bastard Abrams from the CDC across To do so she will need to drain 6 points of essence (meaning that she's draining enough essence to last two years without using any essence fueled powers).
Essence Drain has an addiction rating of Targets Essence + 2. This means we are looking at ratings of 8, 7, 6, 5, 4, and 3. The book is not clear if essence drain requires an addiction test every time it's used or only when the essence drainers essence is higher than (6-essence loss from factors not related to HMHVV). Jen will resist addiction with her Logic (

+ her Willpower (6) or 14 dice.
Ok, so she needs to make a test against a threshold of 2 every time she essence drains. That means six tests. Time to go look at the edge rules, the only way this character is failing this test is a very unlucky roll.
Jen now has an addiction threshold of 2 to essence drain. It will go down to zero if she doesn't drain anyone for the next two weeks. On the other hand if she drains someone on each of the next three consecutive weeks (11-8) she will have to make a bonus addiction test.
These rules seem like they were designed to make for slow addictions.