While a global population of five, six, seven (or whatever) billion is sustainable today (and quite easily: the problem of famine in the modern world is a problem of distribution), a global population of that sort of size in 1314 would not have been. Malthus was fundamentally wrong about several things, but what turned him into the laughing stock of later centuries was one of the most important breakthroughs in the history of agriculture (i.e. the introduction of fodder crops) rather than a flaw in his reasoning. Essentially, his thesis was overtaken - and rendered absurd - by events. Previous population expansions in Europe had generally ended famine. And even today there are parts of the world that are clearly 'overpopulated'.
Having said all that, the answer to the question is obviously a resounding no. Contrary to popular belief, wars are rarely fought for basic material resources, and the worst atrocities almost never. To say nothing of the heinous actions of random individuals on other individuals. Rape is not caused by overpopulation.
More or less this.
Note that the countries that have the highest birth rates aren't necessarily the same countries as those with unsustainable patterns of consumption (which could be addressed, in part, by policies that promoted human need rather than economic growth-but that's some Utopian nonsense apparently...)
In other words, Nix, Bacon King, and Al are right.
The key is economic growth and population growth and the goal is to make sure what is impossible today is what is the status quo 50 years from now.