Maybe, but I wouldn't want to take any chances with this. You don't know for sure that the page is unallocated. If it wasn't allocated, the backup shouldn't be breaking as backups only read allocated extents and if the only corruption was in that index, dropping the index would have deallocated the extent.

p.s. CheckDB Taking 8 hours on a 300GB database? That sounds like a serious IO contention problem in and of itself. I've done checkDB of TB sized databases faster than that.