First of all I would like to say that its a good question, and given below are some of the suggestion,
Suggestion.1. For Automated Test Runs, you can enable setting - "Submit a defect to Quality center for each failed step" in Tools > Option > Run Tab >. This is will enable QTP to log a defect for every failed step. Further customization have to be done using VB Script to link the defect to the Test Case.
Suggestion.2. Use WorkFlow Script for the Quality Center Project. To be specific you need to Trigger TestLab_RunTests Subroutine to make this happen.