OK...Letsrun IS as un-educated as everyone says.
I think the issue comes from the fact that there are different genres of emo, and that, as you are lacking the experience in making fun of emo kids, has lead you to not know ALL the types of emo you can crack on.
As reference, here are the major types of emo:
1. Screamo-what most of you referenced. These are emo bands/guys who got tired of being made fun of for being pansy-like, so they adopted traits of 'hardcore'. The only problem is, that they made the 'breakdowns' into 'cry-downs', mixed in some high-pitched singing, and turned down the volume a bit. Be wary of this emo, for it can draw in the weak minded before they realize they are at an emo show.
2. Acoustic Emo (True Emo)- This describes your more obvious offences to the aural senses. Their songs are played on acoustic guitars for the most part. Sometimes will use an electric guitar, but limit the distortion and speed with which they play. Usually heard on the radio by the masses since they are well liked by kids coming out of their teeny-bop phase who want to look cool for all the big cool HS kids. Pretty easy to pick out--just listen for lyrics that are 90% of the time about a girl and 10% of the time about how life sucks because of a girl. This is what Plain White T's falls under, Dashboard Confessional, and your precious Death Cab for Cutie.
3. Misc.- Random bands that do not fit the above two. They DO write alot of songs about getting left by a girl, but they are also filled with verses about getting smashed, or possibly killing that girl in an inventive way. Music style revolves around riffs taked from 'punk' (Remember, Blink 182 and Good Charlotte are NOT 'punk'....), but not played as crazy fast, and slightly more treble. Bands that exemplify this would be Alkaline Trio, as well as AFI prior to them selling out (kinda..), Cursive, and Hot Water Music--but Alkaline Trio is the flagship band for this. If you are going to be emo, be this kind of emo. Probably the least gay.
So to answer the MAIN question: Yes, Delilah is emo. If you like it, you probably have emo-like ways, even if you do not recognize them yet, or are denying them--comonly refered to as being "In The Closet".
And yes, in case someone is 'wondering...', I AM an expert on Emo. I actually have my Degreemo in it.