I assume that the basic assumption of this question is that Egypt, as a strongly Muslim country, will not have its population growth rate affected much by family planning projects. While this may be true, it has not been true for all Muslim countries. Therefore, it is at least possible that Egypt could see a decrease in fertility if it adopts a policy of promoting family planning.
As can be seen in the links below, there is no clear and necessary connection between Islam and fertility levels. Iran is, of course, a strongly Muslim country with a theocratic government in power. Even so, there has been a strong increase in contraceptive use and a decrease in fertility. On this evidence, it is hard to argue that an Islamic country cannot cause its fertility to decline.
It may be that religion will be less of a block to decreasing population growth rates than economic factors. Around the world, increasing wealth and prosperity has typically caused fertility rates to decline. It may be that Egypt is too poor to experience fertility decline, not too religious.