Sure it does... there are single note, chord and combo arrangements. Combo is a combination of single note and chord (and/or double stops). Chord arrangements are chords only.
One song can have multiple arrangements, sometimes more than one of the same type (Combo 1 and Combo 2, for example). Most arrangements are combo. Chord arrangements are the usually the easiest ones, that's why you will find few videos on these. People don't find them challenging enough to post a video on the Internet.
You can go to Rocksmith Buddy and check out http://rsevolve.com/sitestats.php You can sort by type and see all the songs that have a pure chord arrangement. There are a number of fun ones. Any flag as DLC are purchased separately from the game disk.
It's ok but be aware the chord recognition is one of the hardest things for the game to do, so sometimes it is too lax, and sometimes it's far too strict (I'm looking at you gobble).
Also, the full strumming pattern is often not charted. No muted strums are shown for example... So it does work, but I think it does lead and combo versions better. For pure strumming of chords you can learn a lot just from existing online sites, and playing acoustic.