It looks like a dragonfly larvae, they are predatory critters and can eat small fish fry amongst other things however i'm not sure if its large enough to pose a threat to your neons- personally i would remove it and put it in a stream/pond/lake etc if you have any nearby .
Yeah you are correct in your assumption that its a nymph, Dragon or Damsel, looks like a Damsel to me, equally get it out of the tank as it is predatory and will easily take a small neon.
Regards
BigC
-- they do not have the 'feathers' at the rear, and have a bigger rear .. <3
I'd recommend removing it though -- they feed on other insects, small fish, mollusks.. stuff like that. Damselfly Larvae are very, very pretty though. :]