As others pointed out, this is really a tricky question.
I would usually say that after 2-3 listens you usually know whether you like a song or not... But in my experience it's never really that simple. With DT, at least for me, it's even more complex than usual.
I liked I&W, Metropolis Pt.2, Octavarium, the second CD from Six Degrees, BC&SL and SC with just one listen.
The first CD from Six Degrees, ToT, FII and Awake took more listens.
And despite my listening to When Dream and Day Unite over 5 times, I still don't like it...
I talked about albums, but there are some songs that I really never know whether I like them or not:
- A few days ago I took Panic Attack out of my iPod, but today I was listening to Octavarium in my car and actually enjoyed it...
- I don't think I like As I Am, yet I keep listening to it...
- This Dying Soul must be two alternating songs, because I either hate it or love it each time I listen to it...
- For some curious reason I never like Scarred and Voices at the same time, they always alternate in my favour...
- I never cared much for The Shattered Fortress, until one day I listened to it and loved it...
- You, Not Me used to be a song I liked, but not any more...
Personal experience (and ranting) aside, if your friend listens to it a couple of times and really doesn't like any song, then DT is probably not for him (even though no single CD really encompasses all that DT is...)