Awards season is an abstraction unless you are trying to cross Hollywood Boulevard during it. Then it is extremely concrete.
The closures are real and sudden
Around the major ceremonies, Hollywood Boulevard and Highland close for days, not hours, for the carpet build. Streets around the Beverly Hilton and the downtown arenas close for individual nights.
What it means for ordinary journeys
If you are flying out of LAX from a Hollywood hotel on a ceremony weekend, the usual route may simply not exist that morning. Add an hour, and tell whoever is driving you which event is on.
If you are attending something
Drop-off points for carpet events are controlled and assigned, often with a credential. Your driver needs to know which event and which entrance well before the night.
The practical advice
Book earlier than usual. Between January and March, chauffeur availability across the city tightens noticeably, and the Sprinter van is usually the first thing to go.
Dates move every year. Check the venue before you plan around them.