Yes, and in that text, it never specifies that only individual people could be denied that freedom. So an originalist would find that any law that prohibited freedom of speech from any association, company, baseball team, or labor union, would be unconstitutional under the Amendment as written. "Congress shall make no law ... abridging freedom of speech". The law in question in Citizens United most certainly abridged a lot of speech.
Consider a law that said individuals are free to have an abortion but hospitals, surgery centers, and Planned parenthood were prohibited from providing those services to you. Under current precedent. Would you then nod your head and say, well Planned Parenthood isn't a person, non-profits aren't people?