Will food logistics limit the population of a civilization of exclusive carnivores with modern technology?
If you mean transportation and storage, maybe. If you mean, the geopolitical system of food production, very likely.
Would being an exclusive carnivore make it harder for a technological society to enjoy the same sustained population growth that we have had?
Yes, indeed. The agricultural revolution was key for population growth, and hence, ancient technology.
If not, what are likely to be the primary limiting factors?
In decreasing order: climate change/energy sources, peasant labor, drinking water and arable land.
This is a complex question, so I'll try to explain some points and then come back to the answers.
According to Systems Ecology, the limiting factor for the population growth of any species is always the amount of energy it can derive from its environment in a useful way.
For most species, this means that the food consumed delivers more energy to the body than the energy invested in basal metabolism and other activities, including of course, those activities that are meant to obtain food (i.e. grazing, hunting and gathering). For example, if gazelles develop a way to run faster, the cheetah population would narrow to the fastest cheetahs. Then the latter species might either evolve into some sort of faster supercheetahs (who need and get more energy from their environment) or dissapear altogether due to famine, sickness, poor genetic diversity, etc. but that is a different story.
For those species that hunt in group, the rule applies for the whole group: those packs of wolves that are able to catch faster gazelles would thrive, but the species might be endangered for the same reasons pointed out in the case of cheetahs.
For those species that are able to produce their food, i.e. transform their environment in order to catch or grow their food, the energy rule holds as well but it gets more interesting. Bees, ants, termites, spiders, beavers, among others, modify their environment to obtain and store their food, so the amount of energy invested in running the production of food must be lower than the amount of energy delivered by the food produced. The energy needed to maintain the glands and synthetize the complex molecules that form the thread of a spiderweb must come for the preys that the web catches.
When it comes to humans, things get even more complex because our species has been able to use exosomatic energy (energy outside the human body) to produce food. In other words, the energy invested in producing, storing and transporting food does not necessarily comes from the energy delivered to the human body through food digestion. Agricultural tools, beasts of burden, natural and chemical fertilizers, machinery, gasoline, etc. are used in the production of food, but the energy required to produce them comes mostly from fossil fuels, biofuels (bioethanol mainly) and primary electricity (hydro, solar, wind, nuclear, biomass, etc.). These exosomatic sources allow us to grow food in deserts, mountains, and other places where it was impossible to produce it a hundred years ago. If you plot the world population and the world production of fossil fuels over time, you will see that both lines start growing roughly at the same time.
Land, water, soil and the "usual" limiting factors are not an obstacle to our food system AS OF TODAY. Each of these factors can be supplied, enhanced or substituted using the exosomatic energy sources mentioned above. In fact, the current food system produces more food than required by the world population (according to FAO), so edible crops are used for other purposes. There so much corn, for example, that it is used to make ethanol for cars, to feed livestock and to sweeten all kinds of things (that's why you can find high-fructose corn syrup in your favorite soft drink). Since the system is based on fossil fuels, it is clearly unsustainable in the long run but that is a different story.
Feeding humanoid carnivores is a bit harder than feeding humans. However, while it seems doubtful that a carnivore population of 7.2 humanoids would survive under the current energy available to us, it is equally doubtful that they would grow at the same rate that omnivore Homo sapiens did because the amount of energy and biomass required to grow carnivore food is larger.
In a trophic pyramid, only ten percent of the energy contained in one level can be transferred to the next one. Since life is basically made of the same molecules (carbohydrates, proteins, etc), this number is also an approximation of biomass transfer. In other words, you need 100 lb of grass to feed 10 lb of herbivores (even if it's 1 lb of insects), and then feed 1 lb of carnivores.
For carnivores, agriculture would only be the step in the food system. In fact, carnivore humanoids might never had developed such a labor intensive practice in the first place! Why take all that time and energy in a system full with weather uncertainties when you can go around hunting game happily? In fact, hunter-gatherer communities were healthier than agricultural societies, not to mention absence of slavery, plagues, wars and other niceties that characterized agricultural empires.
On the other hand, hunting carnivore humanoids might go extinct after they hunt down every last game available. In fact, humans are held responsible for the extinction of megafauna in all continents except Africa, where elephants, rhinos and hippos evolved together with sapiens, so they "know" that our weak appearance is deceiving and that sapiens are not to be trusted.
Assuming our humanoids did develop agriculture as a desperate means to "grow" their own chickens or something, you would have a though problem feeding carnivore slaves and peasants. Anyways, let's assume peasant labor was fed on a mix of dry insects, blood and bones for some time until some ancient civilization found coal (energy resource) and built some steam engine (technology) that they could apply to agriculture (note we are talking here about two major processes in human history: agricultural and industrial revolution). Even in that case, the rate of growth of the population would be lower because these humanoids would still be entirely on the third level of the trophic pyramid, rather than partly on the second level as our agricultural ancestors were.