Yes, birds can suffer concusions or other brain injury from hitting flying into windows.
Look at his eyes…do the pupils seem normal and equal in size?
Does he show any sign of lesions on or around his eyes or beak/ mouth?
There is an illness called avian pox ( not contagious to humans of other domestic animals, but very contagious to other birds )
Some symptoms of the disease are swollen eyes with lesions ( blisters ) the mouth, throat is effected too, is the bird gaping or gasping, labored breathing?
This disease cause pox to form in the airways and throat and the bird is unable to swallow, an ugly way to go.
If you are able to handle the bird you can tell his general condition by feeling the keel bone ( breast bone ) that runs diagonally down the mid section of his chest.
Birds in a state of starvation or very underweight will have very pronounced keel bones.
Impossible to say, just keep an eye on him/her and if the bird remains immobile for many hours it is safe to assume there is a health concern. Many wildlife groups have members that treat pigeons.
They are not protected by any state laws, but a few volunteers usually agree to treat them.