The short answer
No — avocado is one of the most dangerous foods for birds and can kill quickly.
Why
Avocado contains persin, a compound that is highly toxic to birds. It can cause heart failure, breathing difficulty and death within hours, sometimes from a surprisingly small amount. Every part is dangerous: flesh, skin, pit and leaves.
What to do
Never offer avocado or anything containing it, such as guacamole. If your budgie has eaten any, treat it as an emergency and contact an avian vet right away.