If so, would it be to find others with similar interests, to share things you've made, find news other geeks find interesting, or something else?
Are there any networks you currently use that already meet those needs?
It's sort of like how Hacker News is for "anything that good hackers would find interesting," which sounds like it means something but really doesn't mean anything specific, and probably just resolves to "anything that correlates with the interests of the mods," like every other moderated community. Other than branding, what even is the point of using "Geek" at all?
But to actually answer you question, personally, no. I think there are already tons of sites which cater to "Geek culture" (or nerd culture or... whatever) of various niches, and of course if what you want in HN, but with invitation only, there is lobste.rs. Someone can basically set what you're describing up as a subreddit. I also don't like invite-only communities on general principle.
How would that be different than what we already have... right here on H/N?
Shameful plug (hope this is ok, this is my first HN comment), but I'm also working on a "social network for geeks" but is more specific to developers and designers: https://codebee.io/ It's a big hurdle to keep users active but it's a side project and haven't been able to devote a lot of time.