When the Dummy System lowers onto Shinji, it kind of sounds like an electronic voice, doesn't it? As ZapalacX put it, like a Cylon.
It also, in my opinion, sounds like it was recorded backwards. I've worked a lot with reversing sound and it sounds to me very much like it was reversed after being recorded.
So I recorded it, reversed it, and played it back. There's no doubt: it's a vocoded message, and while I'm not sure, it seems to be in English. It contains non-Japanese syllables and the person talking seems to have an accent that could be considered American.
I couldn't make out what was being said, but Reichu heard "dominated by others". I searched that and found it. It's a quote from the cult classic sci-fi film Colossus: The Forbin Project. It's saying:
"Freedom is an illusion. All you lose is the emotion of pride. To be dominated by me is not as bad for human pride as to be dominated by others of your species."
Coincidentally, I saw the film last year, which makes this discovery all the more powerful. The context is (spoilers for Colossus: The Forbin Project):
The speech that Colossus makes at the end of the film when he has successfully dominated humanity.
File:
http://projectenthalpy.com/forhumanpride.mp3