Sure... manually... but not in code and not automatically as part of a test run. I'm sorry the answer doesn't help much... but that's the answer I have. Again, TestComplete executes tests... MANAGING what gets executed and when it gets executed is what a Test Management tool is for... and TestComplete is not a Test Management tool.
As for moving test items around....
One of the ways I like to explain how a "test run" works in TestComplete is that, when you start a test run, there's a "compile" process that happens at the beginning that initializes the "stuff" of the test run... stuff that is loaded into memory BEFORE the tests start executing that control and dictate the rules of execution (stop on error, iteration count, test item dependencies, etc). Part of that "compile" is the list of Test Items to be executed. These are "read only" during a test run because they are "compiled" as part of what you are executing. There are a number of things like this that are "initialized" when a test run starts which is why certain options, configuration settings, etc., are "read-only" at Run Time in TestComplete. So, no, you cannot "move" TestItems into separate folders via code during Run Time of your tests.