Does he care about them? I would think not. Griffith wants his dream and the God Hand's plan is just the means by which he achieves it. Same with everyone else in the God Hand. They may be more devoted to the Idea of Evil's plan, but they have desires of their own that they want out of all this. So I don't think they have a particularly close relationship. They aren't friends or comrades, but they are allies.

My belief about the God Hand (going by the trend with Griffith and the Wise Man) is that they were each people of humble origins in their human lives who flew too close to the sun and were cast down by the governing power of society. The people who would become the five angels who would put into motion God's will for the world had to possess such qualities in order to fit the role given to them.

My belief is that their own plan (which naturally aligns with the IoE's plan) is to overthrow the established power of the world in order to enforce their own. They want to take what they believe they are entitled to while simultaneously getting back at society for casting them down in the first place and fulfilling the IoE's grand design and humanity's collective unconscious desire (which they, more or less, seem devoted to). They're kindred spirits in pursuit of their own selfish desires, and in the process want to create a world that is in their image "perfect" for them to rule. And to that end they work together as a unit to accomplish this goal because it gives all of them what they want.

Of course, most of this is speculation. I could be wrong and they all take the time to go play golf and have barbecues on the weekends.