Running a SQL job from TestComplete

Short answer: yes https://support.smartbear.com/testcomplete/docs/testing-with/advanced/working-with-external-data-sources/databases/ado-requirements.html

Longer answer: There are many different ways of  "skinning the cat".  I prefer to use the various ADO methods and objects to create SQL query objects for executing my SQL tasks and jobs.  So much so that I created a Script Extension which encapsulates my code so that it's always available to me.  

If you don't want to use the extension, there are various examples in the TestComplete documentation that shows the basics.

https://support.smartbear.com/testcomplete/docs/reference/program-objects/ado/createadoquery.html

However, if you want to use what I already wrote, follow the links in my signature block.