According to what I read from the producers before the first episode, Hagman will be in all of the episodes this seasons (10 episodes, counting the 2 the first night).
From what they said, though, he was undergoing cancer treatment when these were being filmed (last year) and they had to re-write some of the scripts to account for the fact that he wasn't physically able to work a full filming schedule (which is supposedly at least 10 hours a day).
My guess is that he'll probably be in it sparingly over the next couple of episodes. But, he'll be in it, none the less. Maybe some cameos where he's talking to John Ross over the phone, etc.
Since these episodes were filmed he is supposedly cancer free and a lot healthier than he was when they were filmed so if the show gets picked up for a second season he should be good to go.
The story lines have been progressing kind of quick anyway so with him "out of town" that gives them the chance to slow it down a tad and let the story develop.