YEs, you can get the Kansai Thru Pass, and it will work, but let me explain the economics of the passes.
A three day Kansai Thru Pass is 5000 yen, which works out little over 1600 yen/day. If you use Hyperdia, you can look up train timetables, and fares. Here is the link:
http://www.hyperdia.com/en/If, for instance, you are in Kyoto, and plan to make a day trip to Nara, you can use Hyperdia to find out when the trains run, and how much it is going to cost. You will find out that it will cost you 610 yen each way on the Kintetsu line, and 690 yen each way on the JR line. (The Kintetsu station is actually closer to the park with the temples.) So, for a day trip to Nara, using a Icoca card and just paying the fare (1220 yen for both ways) is less expensive than one day of a Kansai Thru Pass.
If you are in Kyoto and want to sigthsee, there is a sightseeing card (1200 for one day, 2000 for two) that is also more economical thatn the Kansai Thru Pass.
You might consider getting one Thru Pass to go from Kyoto, to Osaka, to travel around Osaka, and to get back to KIX for your flight. if you are going to Mount Koya for a day trip, it would really pay off. But you need to look at what you are going to do each day,
I don't know where you are planning to stay in Osaka, but you may want to stay near Namba. There are lots of things with walking distance.
http://www.japan-guide.com/e/e4001.htmlIf you are staying in the Namba area of Osaka, and plan to go to Universal Studios, the train fare is 170 yen each way (JR-Namba to UniversalCity line, NOT covered by Thru Pass), or if you plan to go to Osaka Aquarium, the one way subway cost is 270 yen (Namba(Subay) to Osakako). An Icoca card that can be used on either a JR or a Private line is very convient, and just paying the fare is not too bad. The fare from Namba(Nankai) to Koyasan is 1230 yen, so it might be cost effective to use a Thru Pass for that day, and to get to the airport (Namba(Nankai) to Kansai Airport).
And, YES is IS confusing. If you are in Namba, Kintetsu rail uses Osaka-Namba station, JR uses JR-Namba, and there is also the Nanba Nankai and Subway stations.
The Icoca card works on JR, Subway, and Private trains, and on some bus lines, so it is very universal in terms of getting around. That's why I recommended it. Gettting to and from the airport is costly, and, depending on where you are staying, the Haruka pass can pay off.
I put the qualifier on the Haruka pass just becaouse IF you decide to stay in the Namba area of Osaka, I think the Nankai private train is the best transportation option from the airport. The Haruka Limited Express train, which goes from KIX to Kyoto, with stops in Osaka, is better for other locations.
