The general answer is Yes. However, there are some states where this may reduce or prevent any recovery. For example, in California, if you did not have valid insurance at the time of the accident, you are only allowed to recovery economic damages, such as medical bills, loss of wages, etc. However, you will not be able to recovery money for pain and suffering, deformity, etc. Accordingly, it is always a good idea to have full coverage when you ride. In addition, also make sure you have limits that meet or exceed $100,000 if possible.