I'm not an expert whether there's an Intl school or not, but I can tell you that the Abha-Jizan reagion in extreme Southern KSA is very remote, and the towns are small and I would be surprised if there was an Intl school anywhere in the province, as the entire region was once part of Yemen, and taken over by KSA in a border war not so long ago. The region is culturally Yemeni, not Saudi, and a bit 3rd worldly compared to the rest of the Kingdom. That's not to say there isn't an International school in Abha, but I would be surprised if there was.
I am likely to be moving to Abha - although I cannot confirm if their is an International School there I would think that there will be one in Khamis as there are a lot of "western" company offices there supporting the airbase. British Aerospace has an office there and there is a British Consulate. I understand the university in Abha has 20 000 students with many expat lecturers.