Well, let's try to shed some light on the subject of the original poster's question. (See? You blurted another response without understanding the context... again.) Samsumg released the kernel mods for the Gear a couple of weeks ago. So CM should eventually run on the Gear, itself. However, that is not necessary in order to integrate the Gear with phones/tablets running CM. For that, all that is needed is the external interface API. Not sure if that's been published yet or not. But with that, Gear/CM integregration should be pretty straightforward. (Similar to that other Samsung-specific feature, the S-Pen, which was picked up by CM very quickly.) So I'd expect to see most any CM-supported device integrated with the Gear in the not too distant future, if it hasn't been done already.
Regarding the Note III... none of its incremental differences from my Note II impress me. 2.7% larger screen? 3.2% larger battery? It's essentially the same phone. I'd be stuck with the initial, rough around the edges, initial release of the stock ROM, without even root access. (Only the International and T-Mobile versions can be rooted, at present.)
Regarding the Gear... it's a pretty limited device compared to, say, the Omate TrueSmart, which can both integrate with CM or act as a completely standalone device, including phone functionality. Compared to the Gear, it has a faster processor, double the RAM, and equal flash out of the box. (But unlike with the Gear, that's expandable.) Not to mention a 5MP camera compared to Gear's 1.9MP. With a 600mAh battery, compared to the Gear's 315mAh, It has substantially better battery life. (Perhaps 2 days between charges rather than requiring a daily charge.) The Omate's IP-67 water/dust resistance rating is good for immersion up to 1m for 30 minutes. (In contrast, the Gear's IP-55 rating means that it should be able to handle hand-washing, but no immersion at all.) And all that for the same price as the Gear.
The Note III/Gear combo is just so far inferior to the Note II/CM10.2/Omate proposition that I can't imagine anyone who did their research beforehand opting for the former. In comparison, the Gear just seems more like a toy.