Do anything to keep fighting - absolutely! This is the default mindset and MUST be so ingrained that it is almost instinctive.
This is one of the greatest skills combat sports develop. It is developed to the point that you see people who are knocked out still 'defending' themselves or swinging as they go down. I quickly figured out there are two types of people in boxing. The guys with experience who will hardly blink as you punch them in the face and will just instead use that as a chance to hit you. And the guys who close their eyes and turn their head away when you punch them in the face, and they get knocked out. I strive to (well actually I strive to not get hit) be the first type of guy.