No, you have to win something to be considered elite. And winning trophies at Celtic in a then-one team league doesn't count (his European record with them is pathetic). But he's done well at every club he has managed, except a stint with Reading.
Last season Leicester finished 37 points behind Liverpool and lost 12 games, so that is not close to elite, but they have definitely grown under him after the inevitable come down post-title-winning season. This season it's open because there is more parity and randomisation thanks to Covid. Look at the table and see they are top at the halfway stage having already lost 5 games and conceded 21 goals. Man Utd have conceded 24 goals in 18 games and are a point behind. That trend would see you nowhere near the title in a normal season.
The manager takes a lot of praise when teams do well but they've also signed well in positions they needed to. Ndidi to replace Kante, Mendy as well. Everyone knew about Tielemans but they took a chance on him. James Maddison was a standout young player in the Championship. Ricardo Pereira another known name but they went for him. Fofana and Castagne are good signings. And they develop through their academy (Chilwell, Barnes, Choudhury). They also signed Harry Maguire and Rodgers helped develop him. He's good at doing this, as we saw with Liverpool. Perhaps his biggest strength. In fact he said it himself recently; "My yardstick has always been about influence, how I can influence players and develop them. Winning trophies for myself is not at the forefront of my mind. There are a lot of great managers that never get a chance to do it."
Any normal season I still think they'd be hard pushed to finish top 4, but there are some teams struggling with the season as it is. The season is open and by default he'd be considered elite if he wins the league. With Ranieri people see it as something of a one-off or fluke season, but if he could add a PL title to cups with Celtic, his Swansea record and a near miss with Liverpool, then he'd be considered elite and probably end up moving to another team.