Will my cat be okay eating food that might be dirty?

It is not really different than humans eating dirty food.

Will she be okay? Sure, she won't die. It is no different than unfortunate people trying to find something to eat from garbage bins. If this continues for a long time, it will create health problems which may reduce the life expectancy. If it is a one time thing, it won't cause any problems.

Can she get sick? She might, but younger cats with good digestive tracts are resilient to such problems.

My suggestion is to check if there is an obvious piece of dirt before feeding it to the cat. Maybe you can use a strainer to reduce the dust.

Also, trust your cat. If she shows an aversion to the food, it means she finds it too dirty. If she leaves out more food in her bowl than usual, it might be a good idea to not to feed it to your cat.

Disclaimer: I am not a vet.