I don't think they're related, the film was almost ready to release when the hack occurred meaning they had a final or very nearly final cut.
I am a sound editor on features, I worked about 9 months at Sony this year (on Fury and 22 Jump Street mostly, not Interview). They can replace music days before the movie is released, particularly now because most shows are distributed almost exclusively on DCP. It's not unusual to printmaster the movie (finalize all the sound) and still not have all the music deals in place. Music is an independent process from the "final cut".
All of the PCs at Sony were still down in mid-December, nobody in any of the administrative departments could access any of the work they'd left on their machines or on servers prior to the hack, everybody had to lug in their Macbooks to get any work done -- Macs were unaffected by the hack. I can't imagine how they could have dotted all their i's for the delivery with one days notice and no corporate PC infrastructure.
Alright, I can buy that. I would have assumed the music got finalized earlier, but I guess you have a lot of options when it comes to the soundtrack. I suppose if nothing else works you can run it at double speed and throw in Yakety Sax.