Sure, that's where the protein is. Lots of folks scramble them rather than boiling. Some even scramble them with the eggshells, for laying hens, as a calcium source. (Blender or processor, then scramble, makes this easy.) Don't feed babies eggshells, though.
In healthy birds, any treat should be no more than 10% of the diet. If you are dealing with a sick bird, this is a good "sick time" food, and may be the only thing they will eat.