For me, both the usual soundtracks and the ad soundtrack are playing at the same time. As soon as the missions section is loaded, the ad tune starts to play along the usual jazzy Skullgirls theme.
The ad tune persists even without using the app at all, as another window... Honestly it scared me at first, but in my opinion, that was kinda awesome! Quite of a surprise. Sounds like my device came straight from the future.