Yes, the DLC Characters come with B side music. It's not all known so far, the way it seems, though.
Iori has Arashi No Saxaphone 2 (Arranged) For A side, and Arashi No Saxaphone 2 (NEOGEO Version) for B side.
NESTS Style Kyo's Main theme is:
There's a video of his mission trials that uses this music from Skystage:
But it's unclear if that's used in game for him as a side B, or just the Combo vid creator's taste.
Mr. Karate's known theme so far:
(Says The Tengu Show, but sounds more like
Shihan...)