If I’ve witnessed a hostile work environment aimed at a co-worker who is too afraid to file a suit, can I file?

There is "hostile"in the everyday sense; then there is hostile in a legally actionable sense. The two things are not the same. 
Certainly, in a commonsense use of the word, a manager who screams profanities, etc. at employees is "hostile." But the law lets managers and employers be as hostile as they like: they can be bullying, cruel, mean, etc. and make the workplace h_ll on earth, and that is legal. Employment in the U.S. is "employment at will" and, among other things, that means that employees have no right to a job or to fair treatment at work; but also, they are not locked into the job and may leave whenever they like and seek other employment or just plain quit and not work. The underlying assumption is, if you hate your job or your boss, leave.
There are exceptions, of course, but they are narrow: the law does not let an employer harass or bully an employee due to his or her race, national origin, sex, age over 40, religion, or disability. So if the manager is, say, yelling racial slurs at the employee, or making anti-female remarks, or mocking a disabled employee, etc., that is illegal. In that case, a complaint could be filed with the federal EEOC,  and yes--someone else could legally bring the matter to the EEOC's attention on behalf of the discriminated against employee (though if the victim does not cooperate, the EEOC might drop the investigation or it might not go anywhere, for lack of evidence). 
However, the harassment must because of race, sex, etc. Harassment not due to that is not legally actionable.