Or is it a no-no in general?
Recently I’ve been trying my hand at some short story writing, mostly in the sci-fi genre, and while my family and friends seem to like it I would be interested in ̶t̶h̶r̶o̶w̶i̶n̶g̶ ̶i̶t̶ ̶t̶o̶ ̶t̶h̶e̶ ̶w̶o̶l̶v̶e̶s̶ giving members of the SD a chance to read it and see what they think, and possibly provide some friendly criticism.
Is this even permitted? I don’t think I’ve really seen it here before which is why I’m unsure.
Thank you 
Dunno what the rules are here, but you might try over at Scribophile. You’ll have to give a few critiques before you’ll earn the right to receive one. Commentary is almost always constructive, so no real worries about someone trolling you.
ETA: Oh, and be careful posting here–if the story can be found with a Google search, that burns through your first publication rights (as far as most publishers are concerned), and you’ll only be able to sell the piece as a reprint. Find a forum (like the above mentioned) that requires a password to read the story.
There’s also this section in the registration agreement:
I don’t know enough about the publishing industry to comment on the possible publishing issues that GreysonCarlisle brought up. There are copyright issues as well. While putting your story up on a web page somewhere would technically copyright it, but if someone plagiarizes it, you are limited in what damages you can collect if you don’t actually file for copyright. But again, I’m an engineer, and I am not an expert in copyright or other publishing issues.
From the SDMB point of view, the only thing we care about is that you shouldn’t post the entire story here. Host it somewhere else and link to it. You are correct that Cafe Society would be the proper forum to discuss your writing.
If your short story (or any kind of story for that matter) gets published, you can mention that in CS as well. But if you want to actually provide a link or other info specifying where said story can be purchased, that’s the dividing line for when the post then belongs in the Marketplace.
The story was protected by copyright as soon as Alex wrote it down (“fixed, tangible form”). Without copyright registration, copyright owners are able only to sue for actual damages, which are difficult to prove, and they’re not usually worth the cost of a lawsuit.
With registration, statutory damages can be sought, which can be significant. The copyright holder might also sue for court costs.
That said, only the final version of a work should be registered, and Alex doesn’t seem to be at that stage yet.
As to the copyright clause on the Dope’s registration agreement, it’s unlikely that any but the author actually owns the copyright for any posts made here. That stipulation will likely be interpreted as a license for the Straight Dope to reprint any posts without further compensation to the author.
Thank you for the answers everyone, very much appreciated!