I am not sure if I understand you correctly. What do you mean by "an entire Converted Test". Please give us more detailed information.
In general you can execute a test in Test Studio which is recorded in VS. You can also export a test from Test Studio to Visual Studio.
You can also execute a fully coded test.
Hope to hear from you soon.
If you are using the button "Convert all steps to code" (see the attached screen shot) it creates a Unit test. To execute this test you need to add reference assembly to Microsoft.VisualStudio.QualityTools.UnitTestFramework.dll.
See this video for a demonstration.
Hope this helps.