No it cannot as it was already said by others, but it is possible to execute commands on the linux machine from TestComplete test code and obtain results. E.g.: https://community.smartbear.com/t5/TestComplete-Functional-Web/Executing-UNIX-commands-through-SSH-in-TestComplete/m-p/61001#M2316
(The more you describe the actual task/plan/need, the more useful answer you might receive...)
Based upon the System Requirements my initial response would aim towards "no". There's a lot about TestComplete that depends upon a Microsoft Windows environment for execution and operation, at least as I understand it.
Short answer - no.