In word, yes. It would be impossible to run your business with full peace of mind if you didn't have the right cover in place. If you were to have an accident whilst on the job for example then you'd want to know that you'd still get an income if you were unable to work for a period of time. Then there's liability claims, both from the public and employees. These types of claims can be devastating if you don't have the right protection.
Tradesman insurance is usually covered when you’re employed by someone else, but its worth checking this with your employer.