After some thought, he seems to fit the description of a Byronic Hero, a very specific type of anti-hero which could be best summarized as "Anti-'Hero' in name only".
Here's some quick sources if you want to look up a better description:
From the Wikipedia article, we have this list of traits which are commonly associated with the character type (I've bolded the ones which I'm more or less certain Gendo has, some explanations added in italics):
- a strong sense of arrogance (hard to tell, could just be that aloof & distant)
- high level of intelligence and perception
- cunning and able to adapt
- suffering from an unnamed crime
- a troubled past
- sophisticated and educated (iffy, he's smart & clever... but his technical knowledge could be moreso by osmosis than formal education; and he was a bit of a thug during the flashback of episode 21, before marrying Yui at least)
- self-critical and introspective
- mysterious, magnetic and charismatic
- struggling with integrity
- power of seduction and sexual attraction
- social and sexual dominance
- emotional conflicts, bipolar tendencies, or moodiness (has some clear conflicts, but is that emotionally distant that it may not qualify)
- a distaste for social institutions and norms (his uniform is always open and otherwise unkempt)
- being an exile, an outcast, or an outlaw (during his earlier years, definitely)
- "dark" attributes not normally associated with a hero
- disrespect of rank and privilege (clearly doesn't care for SEELE's plans other than to use them to his own ends)
- jaded, world-weary
- cynicism
- self-destructive behaviour (trying to start Third Impact, neglecting Shinji, etc.)
So yes, he fits the vast majority very well. The TV tropes adds a few other traits which fit him quite well: a loner, prone to brooding (a.k.a.: introspection, navel-gazing), quite often a Magnificient Bastard, and just could potentially be redeemed by love (which could be the case before Yui was absorbed by Unit 01)..... and the consequences of when that love is lost.
So could Gendo Ikari be consider a Byronic Hero, an anti-"hero" (if in name only) solely because the nature of the narrative has him do (or at least give the orders for) heroic actions? Or perhaps a good example of one who went too far over to the dark side (a fallen or tragic hero) to be considered not even remotely heroic despite his (somewhat) noble intentions?
Or how about all of the above?