Not completely because humans can self-regulate population growth using their intelligence whereas bacteria cannot (as far as I know, I could be wrong). There are many different theories about this and I will talk about them and see how they pertain to you theory.

Malthusian Theory

Proposed by Malthus which is that human population grows exponentially while food production grows linearly and the math doesn't quite add up so there will be massive death under current trends. However dear old Malthus proposed this right before the industrial revolution and he has been proven wrong by the agricultural revolution which massively increased food production with use of fertilizers created through the Haber process and the mechanization of farm equipment allowed increased production. However his general sentiments still ring true as we reach a population near 7 billion and 2.5 people are born every minute, and almost all population growth is occurring in the developing world where resources are already exhausted.

Carrying Capacity

D.J. Bogue first proposed this with the idea that we are living with a phantom carrying capacity, in terms of non renewable resources that were stockpiled before human civilization and will not be replaced anywhere near our rate of their consumption. There have been predictions that as these run out there will be massive conflict, death, and environmental destruction over dwindling resources, however there are optimists who say that humans will adapt and switch to new resources before we reach that point just as the industrial and agricultural revolutions allowed us to support a much larger population then we ever thought possible, although it may have only delayed inevitable disaster.

Is your theory true?

I say no, because I think humans have the capacity for self regulation. In developed countries, birth rates are already below replacement fertility (2.1 women per children) and the populations would shrink if not for the influx of immigrants. With industrialization, urbanization and the invention of modern medicine people are living longer and not needing so many children to account for those that would not live to bear children. The invention of vaccines and modern medicine dropped the death rate dramatically while the birth rate remained high for a generation or two causing population explosion. However once people had the paradigm shift that they did not need as many children the fertility rate dropped and population stabilizes. Google image the demographic transition model and you can see how population naturally stabilizes over time as the populations adjust to death rates.

The problem

Almost all population growth will be occurring in the developing world world over the next century. There will be conflict over resources such as food an energy if their country cannot support the population and does not have the economic means to import resources as the developed nations do. For instance the UK has over six times the population what its land can support (for current population and resource consumption), but its economy allows it to import food and resources to support it and so it is not overpopulated. Overpopulation occurs when there are too many people to be supported, and the unfortunate fact, as is now being seen in countries like India, Pakistan and most of Sub Saharan Africa, is that there will be more deaths resulting from overpopulation induced poverty. There will not be an entire human population collapse, only a population drop in the developing world after it continues to increase. Hopefully this was helpful.... if anyone managed to read all of it.

No, the human population would only decline until it no longer exceeded the carrying capacity.

I think we're smart enough to prevent complete extinction from such a cause. We can regulate population or create new resources. I don't think the human population will last forever, but I don't think this will be our destruction

It wont be quite just to say that human population would reach an end so foolish. I mean we have used all are smartness in varied places.. We've made bombs.. We've made Terrorists out of Human beings.. We are destroying the natural phenomenon at a steady rate and we're a part of a humongous race to reach someplace or fulfill an ideal so scarce. We should leave the end to ourselves. We don't need nothing else but ourselves to be extinct.

In the example the bacteria eats all the food, then there is none left so they all die.

ie, there is no food production.

With humans there will still be food production, and the population that exists will at its max be equal to the number of people such as food production can support.