Yes they can kick orgs in certain cases. In normal situations tho, due to bad performance they can only kick an org every 4 years. Basically orgs signed 4 year deals and in 4 years riot decides if they want to renew or replace. We're on year 2, so that won't be the case until the 2026 off season
It's a long time that's the whole point of franchising, giving orgs an stable situation to work with, no constant pressure and the possibility to build for the future like teams like many teams are doing with young talent. If Riot could kick orgs at any time many young tier 2 talents wouldn't have been picked up in the first place