Twice in the past year I have given a friend a resume to give to one of the head guys at their job. I don't know and doubt that they even went through HR. Now I am filling out an application and came across the question about having applied for the company before. Does me giving the friend the resume constitute as applying for the company before?

No, it does not. If you did not submit an application for employment to the HR department, then you have not applied to the company.