Yes they’re are effective against DEATH or severe COVID. Some hospitalisations are inevitable. No two humans are the same. There is no silver bullet. Just because you’re in hospital doesn’t mean it’s necessarily severe disease. Depends on the state’s relevant policy. Qld I believe will admit you if you are COVID positive but I’m not 100% sure on that. Each state or country has varying requirements for admission.
From the CDC
https://www.cdc.gov/mmwr/volumes/70/wr/mm7018e1.htm
“In a multistate network of U.S. hospitals during January–March 2021, receipt of Pfizer-BioNTech or Moderna COVID-19 vaccines was 94% effective against COVID-19 hospitalization among fully vaccinated adults and 64% effective among partially vaccinated adults aged ≥65 years.”