No. The completion certificate simply confirms that, as far as the Local Authority has been able to ascertain, the work on-site complies with the current Building Regulations. This means that inspections will need to have been carried out at the appropriate times, and that any problems found were put right. The Local Authority does not provide a guarantee or warranty on the work.
If you are buying a new or altered property, always make sure your solicitor checks that a completion certificate has been issued for the work. This is particularly important as if defects are found later; it may be you who is responsible for correcting them rather than the previous owner!