Some of it, but not all of it. At stage 1 you have -no- debuffs, at stag 2 you see 15% more fire damage. At stage 3, 20% and stage 4 25% (just food for thought, used to be perpetually 40% in all stages).
As a dunmer, you get some 3000 fire resistance. I forget the exact math, but it's something like 600 resist is 1% reduction. That means that at stage one you're actually 5% flame resistant, where at stage two (PvE DPS/healer) you are 10% weak to fire, 15% at three (PvE tanks), and 20% at stage 4 (PvPers, typically).
If you were in stage one vampirism, and took a 5k flame attack, it would do 4.75k (super loose math) at stage 1. Stage two, the 5k hit is a 5.5k hit. 3, 5.75k. Stage four, 6k damage, as a dunmer.
Honestly as you level champ points you'll notice the damage even less, as you can spend points into a tree called elemental defender to reduce incoming flame, frost, shock, and magic damage. Mime hovers at 17.5%, which means as a vampire in stage two my character is actually receiving 7.5% less damage than a base character, but still 10% more than a non vamp. To me, worth it entirely.