Small test app using Yii 1.1 with ERunActions extension to test this question.
Setup:
- configure Apache virtual host with document root pointing to app/ (example is below)
- add 'yii-test-runactions.lc' to the hosts file
- open http://yii-test-runactions.lc/index.php/test/index
Now click the 'run' link and check the /app/protected/runtime/application.log, it should show that all three actions (Index, TimeConsumingOperation and SendMail) were invoked.