"Taking Over Me" disagrees. "Whisper" and "My Last Breath" are better, too. In fact, I wouldn't even put "My Immortal" in the top half! But it's still flawless, this whole album is perfect in my opinion.
I don't know if I'd call the album iconic but it certainly earned them a place as one of the defining rock bands of the 2000's.
When people look back at what music they were into back in middle school in the early 2000's, Evanescence (aka BMTL and My Immortal) will probably come up. But when people look back at the most important and remembered albums of the last decade, Fallen will be nowhere to be found.