Can test automation improve test effectiveness?

Yes, Automating a test makes the test process: 
1.Fast  
2.Reliable 
3. Repeatable 
4.Programmable 
5.Reusable 
6.Comprehensive

     Yes absolutely.
 
         Improve the Testing Process
         Define Requirements
         Prove the Concept
         Champion Product Testability
         Design for Sustainability
         Plan for Deployment
         Face the Challenges of Success

Yes..

Well automation is not a magic wand for all testing vows, the requirement has to be clearly studied and a ROI study conducted to see if automation will bring the expected results. For projects that are long term and having multiple regressions automation is a good choice..

Yes Exactly b'coz there will not be any human misatkes, time saving, low resources (human resurce) and moreover we can do regression testing very easily