the idea of nerds (freaks, geeks, whatever) lacking hygene isn't new,
if i think about a stereotypical nerd, he has long or poorly cut, unwashed hair, a face covered in acne, most probably thick glasses and of course sparely growing, nasty, curly hair (looking like pubes) covering the lower region of his face (and probably double, triple, quadruple chin).
now, why do i imagine a nerd like that?
because i, although not completely un-nerdy – excuse the shameless euphemism here – just reproduce the image of nerds as shown by the media, and so i think a stereotypical nerd must be smelly, competely ignoring his looks and hygene, and either fat or skinny. so i don't know if the stereotypical nerd evolved beyond paying attention to physical appearance (because waifu loves them just the way they are… erm… well… at least mine does so) or he just doen't give a shit/ has no time to care about it because of declining loading times and doen't want to loose any of his precious gaming (or whatever nerdy he's doing) time.
now to the neckbeard, people with weak growth of facial hair, can't grow a proper full beard, so the best thing would be just to shave the meagrely growing hair off. if if a person like that doesn't shave for "reasons" (like, er, very time consuming hobbies) neglects hygene and looks, they don't shave at all.
imagine a person having a double chin, making the neckbreard even more visible
notice how your attention wanders to the neck/chin area.
it's just a repulsing characteristic of a person that doesn't take care of his (or maybe her :O ) looks, just like unwashed hair, body odor, uninhibited growth of pimples or gain of adipose.
so if i would call someone a neckbeard, that would imply tat i think this person invest so much time into something that he/she neglects hygene (an most likely social contacts…) with nasty ass facial pubes, of course i could say nerd or freak or geek, but neckbeard also insult's the person physical appearance, hygene etc. and not just his time spending habits.