Would already having professionally (not self-published or paying someone to have it published) published short stories help give you credit when looking for a literary agent or publisher?
What Kyll said. Previous publishing creds in nearly anything reputable are helpful because it means someone gave you the consideration and found you worthy. With luck, as Kyll mentions, it means you're selling.
At least as far as the speculative fiction realm goes, it can also be a way to get noticed. Which is wonderful.
Reputable contests and publications are the key thing, though. Publications that take just about anything--likely the ones that don't actually pay you--can look just as iffy as self-publishing.
And, note for anyone reading this, if you don't have previous pub cred, no worries. Just don't mention it in a query to an agency. The agent will know by your lack of saying anything that you don't have any cred, but that you have done your research on querying and aren't attempting to whine about how good you are even if you're unpublished and how your dog thinks your books are just great.
I don't fangirl. I fandragon.
Have you thanked a teacher lately? You should. Their bladder control alone is legend.
It also isn't unheard of for agents and editors to contact you after seeing your work in a (reputable) journal or anthology. I have a professor who had several writer friends that this happened to.
Publishing is a business, and it's all about marketing yourself and showing editors/agents that what you do is what readers want to see.
