Demian,
I posted a response back from Samsung regarding this in another thread but I am going to re-post it. Disappointing response to say the least.
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Dear Alex Martin,
Thank you for contacting Samsung Telecommunications America.
After reviewing your Email, we understand that you are able to Sync S-Health with Gear 2 Neo using Samsung S5 and not with Note 3.
We understand your requirement.
We have checked all the available resources from our end and we are unable to speculate when/if S-Health will be Synced with Gear 2 Neo using Note 3 might be available due to the fact that this might lead to inaccurate information and confusion. Should this become available, it will be posted on our website.