Are lunar occultations visible to the naked eye?
Yes - especially as the occultation does not have to occur on the bright side. Planets may also be occulted (see http://www.lunar-occultations.com/iota/planets/planets.htm)

Incidentally the symbol is not originally Islamic. It was the flag of Constantinople when conquered by the Ottomans and then adopted by them. The Ottomans later became the Caliphs - the nominal leaders of the world's Sunni Muslims and so the flag was widely adopted across Islam.