No, it's like Leprechaun Returns but none of the other sequels (2, 3, In Space, In Tha Hood, and Back 2 Tha Hood) were tied to the original 1993 film whatsoever. Returns is actually the first and only true sequel to the first Leprechaun film. The two Candyman sequels were actually connected to the first one, even the awful 3rd one was connected to the 2nd one and features the little girl from the end of second movie, all grown up. Funny how neither of those horror franchises are alike, other than both being slashers. One is a horror comedy and the other is pure horror with little to no dark comedy, whatsoever.
The reason why the Leprechaun sequels, made from 1994-2003 had no connection to the first, was because it would show the Leprechaun still alive and within completely different scenarios, and none of the events from the previous films carried over. Like how the hell did the Leprechaun get from Las Vegas to outer space, between the 3rd and 4th films? Also, Tha Hood sequels say he was turned into stone, during the 1970s, where in the first three films (ignoring the 4th one) he was defeated back in the 1990s, three times by completely different survivors. Leprechaun Returns actually acknowledges the events of the first one and shows that the Leprechaun was defeated and thrown into a well and came back to life, 25 years later. The actor who played Francis from Pee-wee's Big Adventure played another manchild character in the first one and he reprises his role in Returns, only to be killed off when The Leprechaun comes out of his body (a la chest burst from Alien).