NOTE: If it's NOT on the list, it doesn't work. We've tested (just about) everything conclusively. Some perks are kinda iffy (or totally irrelevant), like the lockpicking perks or Warmaster in the two handed tree. If anything is affected it's only the percentage chance of it activating, and that rounds down to 3% of the time. Nearly impossible to accurately test.
Alteration: Atronach - Yes - Tested on pc, 30% spell absorbation chance becomes 37.5%
Magic Resistance - Yes - Again, tested on pc, 30% magic resist becomes 37.5%
Enchanting: No perks affected.
Smithing: No perks affected.
Heavy Armor: Only fists of steel More than 68 unarmed damage is now possible.
NOTE: Reflect blows: testing the chance of it happening was inconclusive.
Block: I can't say for sure, but elemental protection did not appear to be affected. Hard to say, as I was a breton to test (so less damage is harder to notice)
Quick reflexes = yes. No other perks affected. (note the time is 'slower' that's the effect)
Two Handed: No perks affected (inconclusinve on percentage chances like warmaster)
One handed: Dual Flurry - Yes - Tested on pc. Weaponspeedmult goes from 1.35 to 1.69. A very significant difference. Normally Weaponspeedmult is 0 but with that perk becomes 1.35 which is 135% but the Necromage does 25% of the whole 135% resulting in total of 169%, almost double! (same issue exists with percentages here as well)
Dual Savagery did not appear to be affected, but I had some trouble testing it, and will update once I figure out a way to test it better.
Archery: Steady hand* bugged, do not use. Possible that one rank is OK... more testing needed. Your ability to shoot arrows effectively while zoomed is essentially removed. Take it BEFORE your a vamp, before necromage or DON'T take it.
Quick Draw - Yes - Tested on pc. Weaponspeedmult goes from 1.30 to 1.63. Same situation as Dual Flurry.
Power Shot - Yes - Tested on pc. Staggerbonus goes from being 0.25 to 0.31.
Light Armor: Only windwalker (NOTE: percentage based problem again). Took 12.3s to fully regen with Necromage, 13.3s without Necromage. Also matches stamina regeneration formula. 5% per second regen without perks, 7.5% with Wind Walker and 8.125% with Wind Walker and Necromage. (2.5*1.25 = 3.125 + the original 5 = 8.125%) Difficult to test 100% due to human error.
Sneak: Muffle = yes (inconclusive, tested over and over, but I was having weather (cloudy/rainy etc... problems so I ragequit... ) (but this is STILL only 75% muffle and not 100%) No other perks affected. This includes sneak attack perks.
Lockpicking: It APPEARS to affect the lock perks. Others cannot be tested or are irrelevant. I measured the distance between the points (on the TV screen) where the pick would wobble slightly WITHOUT a vibration on the controller. It appeared bigger, but this is essentially impossible to confirm. Used the same lock, but clearly had to "back out" of the lock to reload the game. Either way, it wasn't significantly easier to pick locks).
Pickpocket: Extra pockets works, light fingers + other perks not affected.
Speech: No perks affected
Alchemy: No perks affected
Illusion: None* Note however that your vampire bonus is seperate from the perks, and that if you've got master of the mind, you can hit higher level undead (having necromage) than otherwise possible.
Conjuration: Atromancy - No - However, the Necromage perk boosts the duration already by 50% and Atronach does stack with that bonus. So 60s original, with Necromage 90s and then with Atromancy 180s.
Restoration: Recover - Yes - With both perks of recovery, macgika regenerates 62% faster.
Avoid Death - Yes - Recovers 312 health instead.
Note some things here. No 5/5 perks are affected so you can make a decent build while you are leveling/questing (Companions and Dark Brotherhood should be done first, as Companions removes vampirism, and the DB has a bug pretty far along that stops you from completing a quest)
Also, getting to 70 restoration for the necromage perk can leave you pretty vulnerable in combat, if you grind your way up there first thing.
I thought a lot more perks would be affected, and we were BOTH surprised by some of the findings (really fists of steel?) Anyway, if it's not on the list it's not affected or totally irrelevant (like wax key and unbreakable in lockpicking). Also, I couldn't find a way to test the speech perks on the right side of the tree, but the others definitely don't work.
Hope it helps you all. We researched this all on another forum, but I figured I'd share the wealth. Also, I did my testing on PS3, if that makes any difference.