Hi,Since the buses on Koya are Nankai, it should be covered by the Kansai thru pass.
However, I'd recommend the Koya Free Servic (or Sabic) pass instead. It's about 1000 yen cheaper than the 2 day Kansai thru and covers the same places in Koyasan. Besides, unless you have a long trip on a third day on a non-JR train line, then I find the Kansai thru pass not worth it.
You can get the Koya Free Servic at Nanba station and it comes with some coupons for free tea at Kogobuji and some reduced admission at a couple of other sites.
And if you decide to get the Koya Free Servic, make sure you buy the non-limited express pass. This regular pass is pretty much the same as the limited express pass, you take non reserved trains and transfer once at Hashimoto.