tl;dr: Given the extremely fluid nature of myth and folklore, it's always possible that the leprechaun's need to count salt was worked into one at some point in the past. However, as someone who both grew up around Irish folklore and did a thesis paper on Germanic & Celtic mythology, I can tell you that I've never seen it mentioned in any of the Irish folk stories I've heard/read.
Leprechauns are usually considered the Irish version of the faerie creatures, and there are actually several kinds: leprechauns, which are a kind of mischeveous shoe maker; clurichaun, which are a perpetually drunk version that likes to guard wine cellars; and a far daerg, which is a more evil type that likes to steal babies. (Interesting but off-topic side note: leprechauns in folklore usually wore red coats; the modern image of a leprechaun is basically just the British stereotypical image of a Irish person, shrunk down a bit.) Later attempts to formalize medieval folklore (e.g. by people like Yeats) usually puts them into the category of "solitary fairy" and assigns a number of common fairy traits to the leprechauns.
Among those common traits, a lot of folklore revolved around how to protect yourself from fairies, especially the ones that wanted to steal your children. The most universal form of protection was "cold iron", which has always been a traditional way to ward off all sorts of supernatural entities, and was supposedly poisonous or acidic to leprechauns. Other common ones I've read about include running water and various herbs/plants; in particular, in Irish lore, four-leafed clovers were said to ward off leprechauns (or possibly allow you to capture them and get their 3 wishes).
As far as I am aware, though, nothing about salt was ever included in the common forms or leprechaun lore, or any other type of grain, seed, etc. That, as you mentioned, is one of the lesser-known vampire weaknesses, one almost absent from modern urban fantasy, since it tends to make vampires look silly. However, there are stories that portray true leprechauns as being obsessed with gold. (They spend their time digging for stashes of gold buried during "times of wars long past"). I'm pretty sure, as a kid, that I've heard at least one story about someone escaping from a leprechaun by throwing a bag of gold at it, which it will immediately stop, count, and add to it's own trove.
At best, if you want to try to find a mythological basis for Supernatural's depiction of leprechauns, we might surmise that writers knew of this vampire salt-counting weakness, but decided that it didn't fit with their very aggressive and dangerous vision of vampires. They also knew of the leprechaun's obsession with counting gold, but realized that the boys were unlikely to carry bags of gold coins around with them. So they merged the two ideas together, figuring that making a one-off monster like a leprechaun have a silly weakness wasn't nearly as big of a deal.
