First in answer to your title question: Yes, you can be sued for what you write in a letter. But you would not be sued for "slander." Slander is the oral or spoken form of defamation. Libel is its written form.
That said, unless in the private letter to the company you singled out a specific person or specific people as being unethical or corrupt, the private letter to the company could not be the basis of a successful defamation claim. You have caused no harm to the reputation of the company.

