Yes pelicans do sometimes eat birds when they are hungry enough.
I've seen a pelican eat a bird one day at a park.
The bird was walking on the ground and the pelican quickly snatched the bird and ate it.
So yes pelicans can and will and sometimes do eat birds especially the smaller birds.
Although birds are not it's main meal choice as pelicans mostly prefer to eat things such as fish, lizards, frogs, crabs and lobsters.
A pelican usually drowns the prey they eat including the bird by filling their beak with water and then it swallows the bird or whatever it's eating.