False again. In a stable sexually reproducing population, there needs to be more than two offspring per couple.
While there may be a need to have a bit more than 2 due to chance deaths, that does not alter the situation. In a population of 1000 those having the mutation will be 1/1000 of the population. In a population of a million those having the mutation will be 1/1,000,000 of the population even in cases where the population increases. Therefore the neutral mutation will not spread and there will be only a very small chance of a 2nd, 3rd, or 4th mutation which will be helpful occurring. The likelihood is that the mutation will dissappear because of the fact that the overwhelming amount of mutations are detrimental.