Kendrix: In this situation, he's wondering about whether he'll live to see the next dawn or not. I don't think this scene has anything to do with this.
( It is worth mentioning, though, that Rebuild expands this scene with another instance of Shinji catching himself glancing at Rei and quickly looking away.)
thewayneiac: What my question boils down to then, is would he have peeked, or even stared, if it had been Asuka's silhouette instead of Rei's?
Kendrix: Shinji generally isn't the type to deliberately go and peek, he's not confident enough for that, and certainly not during the prologue arc - He mostly comes in contact with boobs or other female attributes through outer forces he has little control of and then reacts in one way or another.
It's also hard to compare this to the scenes involving Asuka - Shinji's at a very different point of his character developement when he meets her, Asuka, expecially in her earlier episodes, gets played for comic relief more often than Rei etc...
Sailor Star Dust: Considering how "in your face" Asuka is towards Shinji about her sexuality, I'd assume he would take a peek or have stared, yes. (But possibly still do a variation of "quickly looking away" (like in 1.0) or stammering out a negative/sorry if Asuka would call him out on it.)