If added at the same time maybe.
FWIW I have a Kole and a Tomini in the same 8' tank and have for years. Not as closely related as a Kole and White tail, but it can be done. I also have 4 Yellows and a Purple in the same tank.
Really depends on the Kole. Mine was a total ****** when I first got him. Killed a foxface and a Hippo (Blue) Tang. Reason I have so many Yellows, was to disperse his aggression. It worked, and he has been a model citizen for years now. Most Koles are mellow, just depends on YOUR fishes personality.
You have a relatively large tank, so you can get away with more than most. As I mentioned above I think a white tail probably would be a problem. You might try a Tomini.
An acclimation box is worth it's weight in gold when adding conspecifics. You'll get a good idea within a couple of days without damage to either fish.
That was a long winded answer for "try it and see". Just be prepared that it might not work...