Check the following conversations:
https://community.smartbear.com/t5/TestComplete-General-Discussions/TestComplete-integration-with-TestRail/td-p/93787
Basically, you'll need to work with the API and write some script code to do what you're asking. It's not "out of the box" but the cool thing about the extensibility of TestComplete is that, if you can write script code, you can build your own Script Extension to do what you want (as these users did).
To answer the first half of your question (can testComplete tests be run from TestRails), as mentioned, TestComplete/TestExecute have commandline execution (https://support.smartbear.com/testcomplete/docs/working-with/automating/command-line-and-exit-codes/command-line.html) which is the usual way for executing tests from an third-party test management tool. I am not familiar with TestRails myself so I don't know what is involved but, if it can execute command lines, then yes, you can run TestComplete tests from TestRails.
