I´d have to register only if my taxable income was above the Cypriot threshhold (which won´t be the case for another 16 years due the non-domiciled regulations introduced 2 years ago). As long as this isn´t the case there is neither a point in registering nor an obligation to do so.
Among other things the point of the DTA is to make sure tax residents of Cyprus won´t be taxed again in Cyprus on income which was already or will be taxed in Germany (and obviously make sure that the same is true for tax residents of Germany with income from Cyprus). It also obligates both countries to share tax relevant data in certain cases.