The Ocean Arrow is a JR train, and your 7, 14, or 21 day JR All-Japan Pass will cover every train that the JR West Pass covers. The real question is:
Are you going to have an active pass while you are traveling in the Kumano region?
Since the trains and cable car to Mount Koya are privately owned (Nankai, and not JR), you may not have an active JR Pass when you go to Mount Koya. When you reach Hashimoto, you will transfer to a JR Liner, which is not that expensive. At Wakayama, you can also take a JR Liner to Tanabe, again at a lower cost.
This would follow your original idea. On the following day you would take a bus to Yunomine Onsen, and visit Hougu Taisha. The next day would be a bus to Katsuura. You would then Activate your JR Pass the day that you leave Katsuura, and go to Kyoto.
However... If you HAVE an active JR pass...
I would go straight to Katsurra, and spend two nights there. Then I would go to Yunomine Onsen for the night. My reasoning would be my concerns about snow in early March. Here is some information about trail difficulty of the various Kumano trails:
http://www.tb-kumano.jp/en/kumano-kodo/difficulty-rating/Here is some elevation data:
Osaka is sea lever.
Koyasan is about 800 meters.
Natchi-Taisha is about 500 meters.
Yunomine Onsen and Hongu-Taisha are at about 100 meters, and the trail between them climbs to about 300 meters (this is the Dainichi-goe trail, about 3.5 kilometers, difficulty 2).
I would be a bit leery of walking some of the Kumano trail in the snow. You will have a very good idea of how much snow will be on the trails when you go to Koyasan (800 meters). If you take the train to Katsuura, and then visit Natchi-Taisha (500 meters), you will have a better idea of what the trails will be like.
When you get to Yunomine Onsen, I would try to get there as early as possible to drop off my luggage. I would then take the Dainichi trail to Hongu-Taisha. If you want to hike more of the Kumano trails, your could take the Hossinmon-oji and Akagi-goe trails back to the Yunomine Onsen, both are difficulty 2. The problem is both of these trails go up past 600 meters, and if there was snow on the ground at Koyasan, I would want to check out snowfall around Nachi-Taisha before attempting these trails.
Here is the link to the overview of Kumano trails:
http://www.tb-kumano.jp/en/kumano-kodo/Look at the trails, and imagine walking along them with a few centimeters of snow on the ground. This could be hazardous.
I hope I have properly voiced my concerns.
In Katsuura, I have stayed four times in the Hotel/Hot Springs Resort Urashima. I like the hot springs that are located in the sea caves that overlook the ocean. Katsurra has a large Tuna fleet, and the buffet dinner will include a Sushi carving demonstration from a whole tuna. I can recommend this hotel.
The other comment that I have is:
There is a tourist information center located below Katsurra station. The station is on the second floor. There is usually someone in the information center that speaks English, and will help you figure out if there are any discount bus passes that you can use for getting to Natchi-Taisha and Hongu-Taisha.
I hope this helps.