I have some parakeet and parrot food that I really have no use for as I don’t own a parakeet or parrot. I was thinking about putting it in the bird feeders for the “normal” birds (chickadees and what have you). Can they/will they eat that food?
Seeds probably aren’t good nutrition for a parakeet or parrot, but a lot of wild birds subsist on 'em. In that case I’d argue it’s probably better for your bird feeder than your parrot. Is it pelleted food? I imagine that’s fine, too. Hell, a hunk of beef suet is dandy.
I think most birds would find parakeet/parrot food nutritious. They’ll peck at it and eat it if they find it to their liking. And if not, the squirrels will eat it. 
What are the specific ingredients?
Food for domesticated birds is likely to be lower in fat that wild bird food, because a bird in a cage doesn’t have the same energy requirements. It shouldn’t harm them, though.
Size of the food bits might be an issue for some small birds, but sure, they can eat all that. If the little birds can’t eat it bigger birds or squirrels or something else will. As noted, pet bird food tends to be lower fat than the wild bird food sold, but wild birds happily eat low fat as well as high fat food.
Given that this is the time of year the wild ones are trying to raise babies, any extra food will probably be quite welcome for them.