If you specify a local path, it will be used. If you specify a QC path, that´s where the results will show up. So far, so (un)clear.
If you want to upload to QC a run result that has been generated locally in a previous run, then there is no standard functionality for that. You might be lucky if you explore the API, and find a way to relocate the local run result, but as far as I remember, the API does not cover enough functionality for that as far as I know.
If you want the result to be generated locally during the test run, and then get it uploaded to QC afterwards -- well then just specify a QC path, and execute the test. The run result will be created locally, and, within one huge upload phase at the end of the test run, the result will be uploaded.
So the standard does exactly what you are looking for. It does not, as one might think, create a run result in QC step by step during test run. It is empty until the test run is complete. (This used to be different in older QC/TD versions. There, you could see the progress so far by looking at the run result of a currently running test. Doesn´t work for QC10 anymore imho.)
Generally, for a test to store its run results in QC, the (outermost) test must be part of a QC test set since run results are always associated with a test set (be it the default test set, or an explicitely specified one). For a test to be part of a test set, it must be stored in QC (i.e. in the test plan, or in the resources tree). Thus, it is impossible to store a test locally (like, on the desktop), and sending run results to QC. The run result would be an orphan in QC´s datamodel perspective, as such would violate referential integrity in the database, and thus is impossible to create.
You can, however, create a QC test that calls a locally-stored test, which generates result steps. Since the "outermost" test determines the run results location, running the QC test creates results in QC even though the main processing (and result generation) took place in a locally-stored test´s script code.