The short answer is yes.
It works because every time you click on the Run button, a new independent instance of your model is created and executed in a separate processing task. This way one can take advantage of the many processing-cores available in its computer.
But it is up to you to control where the results (csv, kml, shp files) of every instance of your simulation will be saved. If you run several simulations at the same time, you should at least give a different file name (or folder name) for saving your results to make sure two simulations are not trying to write into one same result file.