Well, yes and no.
No, because you cannot start the song data at a certain time point without going through the song data from the beginning. <writing and own continue music function in this case would be nearly impossible.
However, what you could do is to pause the song regulary becfore going into battle, backup the song and track variables to a malloced area and reload it back after the battle and use the inbuilt continue function. That way you wouldn't need to track how far the song has been playing nor you'd need to write an own continue/unpause function. The only downside is that the backuping the songvariables could take quite a bit of memory. 0x50 bytes per track + 0x40 bytes for the song control variables.
If you think that's a good idea I can tell you more clearly what exactly you'd need to backup and reload to make it work.