The correct answer is - No.
The changing birthrates, be it becoming lower or higher, will not and can not change the development of the country just by themselves. The development of the countries does depend on the birthrates, but it also depends on the death rates, the conditions for life, the healthcare, the availability of resources for the people.
If the birthrates are very high, we will immediately assume that the country will have a bright future because it has a constantly growing young population which will be increasing the labor force, and that is always good for the development. On the other hand, the living conditions may be terrible int he country, resulting in a very high death rates, with lot of infants and young children dying, as well as a very low life expectancy. That will be terrible for the development of the country as the people will be in terrible physical and psychological condition, thus not being able to contribute a lot for the development as they will not be able to work a lot, nor work properly. This is unfortunately the case in lot of the sub-Saharan African countries.