Storytelling is, not only, appropriate in a folk club, it is routine.
I have never done a performance without stories. When I do senior facilities, my set includes the lovely "Believe Me, If All Those endearing Young Charms" precede by the tender story of how it was composed. (Look it up. You'll love it).
When I do a Jewish venue, I mix in stories about Chassidim and a few Chelm tales, of course. My agents sell me as a singer and storyteller.
When I play a folk club or folk concert, I tell the same stories and add a couple from South Philly. What I don't do is announce, "I am about to tell a story." I know how "sophisticated" and jaded a folk audience can be, so I just kind of sneak up on them and, before they know it, they have been enjoying a story.
The thing is, a performance lives or dies on its own merits. A good performance is always welcome, no matter what the form.