Currently Testcomplete does support export to HTML, XML and MHT file. You can do scripting to customize does.
You can also give it a try to Jenkins, it has very good reporting engine.
You may want to check the following article explaining how to export TC reports to see them in Allure created by @Vallalarasu_P:
SmartBear Community and Education Manager
I have a doubt about converting Summary to jUnit. When we have warning test - it is converted to passed test. Allure shows all test passed due to it.
If Test Complete will convert warning to junit error - Allure will show test as broken (yellow).
So, should be next:
Log.Error -> junit fialures -> Allure error
Log.Warning -> junit error - > Allure broken