Far from it.

The world already produces more than is necessary to feed every human on earth. Even if technology didn't improve, (which it is) we have decades before population would grow enough to match production.

The problems with Third World hunger are a consequence of several factors which make the match between world supply and world demand a mismatch.

First of all, mortality through disease is coming down even in those countries. For some time, AIDS looked like it could make a new rise in mortality rates, but it is now clear that was a bump rather than a long term break -- and it never affected to a serious degree most of the regions with the highest growth.

Second, mortality from violence, both crime and war, is also coming down. Incredibly so, but it is. The amount and scale of wars in the 19th and 20th century will probably not be matched ever again, short of a world war involving WMDs. Crime still goes up with urbanization, but goes down again with improvements in justice system's honesty and forensic science.

These both leave more available people to die of starvation who would have been killed by disease or violence in older eras.

Then come the factors which are direct to food supply and demand.

For the most part, food production is concentrated in rich and some middle income countries. This is because today food production depends as much or more from technology based improvements in agricultural and husbandry yields than from having ideal soils and climates. Arid Australia produces more than many countries with better soils and rain - say, Zimbabwe?

But rich countries face trade barriers to export food beyond their own borders, or those of their own trade blocs (as the EU and NAFTA,) because agriculture and husbandry are, everywhere, among the more protected sectors. This is obvious for a government: raising crops and cattle employs a lot of people whether or not it yields enough food, and governments prefer to have these lots of people employed there under-producing, than to open the sector and have more food - but also many unemployed ex-farmers / ex-peasants which can be an inconvenient force full of political demands. And so we have things like the US employing 2% in agriculture producing a lot more than countries employing over 2/3 of their workforce in it.

Btw, Singapore does not have hunger. And it is an island which is today urbanized in its entirety. As an island, it can and does fish. But every food other than fish in Singapore is imported.

Of course, exporting is always more expensive than local trade; so those rich and middle income producers always face rising costs in exporting to poorer countries or regions. Combine this with the lower incomes in the proposed new markets and that alone is a high barrier to entry. But trade restrictions to protect local farmers and peasants only make the whole thing a lot worse than it would be with the quality of modern transportation. And given that the technology behind higher yields in richer countries is itself expensive, it can usually not just be imported directly and immediately. (Not for lack of trying - the Republic of India tried.)

Food aid doesn't help, but not for the reasons you cite. It doesn't help because it disincentives both food trade from higher yielding countries and local farmers from trying to move out of subsistence schemes (in both cases, because aid floods the market with free-to-the-consumer produce.) In turn, governments know that people fed for free are happy about that, but also that food aid only comes if famine is a risk, so their incentive in turn is to never let the threat of famine really go away, or the food aid train will stop coming.

The problem also isn't taxes. The people of the First World are very well taxed. But you will notice that the large majority of those taxes stay inside. Pensions are the main tax receiver in the First World; but everything else: health, police, education, national defense, roads or railways, whatever... is spent at home. Even the highest aid budget is less than 1% - while pensions in some countries are over 50%

So no. Hunger still exists, but it is not because of lack of production; and the local lack of production is neither completely "natural" nor ultimately a deciding factor that hunger exists. And so, population growth is also not a factor in hunger.