No. If you travel from Turkey to another country (Syria or a third country), your protection under Temporary Protection would be cancelled. Although in principle you would have the right to seek protection upon re-approaching the Turkish border gates (land, air, seaports), there are no guarantees that you would be admitted or your application would be processed by the Turkish authorities.
If you wish to exit Turkey permanently, you need to obtain an exit permit from Directorate General of Migration Management through the Provincial Directorate of Migration Management of the city in which you are registered.