Whenever a part of a requirement chain is modified, the status will clearly indicate that some areas need to be re-tested. So, the simple answer is: yes you need to re-test. However, Integrator will let you see clearly which areas are affected and will help you put the ressources where they have the most impact on the project status.
Integrator has an upgrade feature where the new spec is inserted to replace an older version. This process is meant to save you time by updating only the modified requirements.