You can argue that, and it has been argued. E.g. Eric Hobsbawm essentially sees both as an extended version of the same conflict in his Age of Extremes, and he would even lump the Cold War into essentially the same sort of affair as a "short 20th century."

The question isn't whether you can reasonably argue such a thing — you obviously can. The question is what it gets you, and what it doesn't get you, to periodize history in this way. What it gets you is an understanding that these conflicts are essentially linked in terms of causality and culture. What it misses out is a lot of distinctions between the specifics of their origins, and arguably makes World War II a lot more "inevitable" seeming than it might have been (which tends to underplay the role of specific historical actors and choices — for example, if WWII is "inevitable" does that somehow absolve Hitler, by just making him a product of his time?). It also makes for a fairly Euro-centric WWII, as fitting the Pacific side of the war into that framework proves slightly less obvious (though you can do it — colonialism, for example).

One of the analytical jobs of the historian is to periodize the past, to say, "this is what we are going to call 'the Cold War' and this is what we are going to call 'the Industrial Revolution'" and so on. We do this because it helps us see history as trends and not just a lot of miscellaneous events. It can have great utility to understanding the past. But these categorizations are almost always somewhat arbitrary and subjective, because they are not "natural" categories in any sense. So we always have to be careful that they are artificial constructions, made to help us, but they can also hinder us. I have no problem saying that World War I and World War II are part of a continuous conflict, so long as one recognizes that this is a form of argument, and that it can hide some salient differences as well.

You could argue it, but it doesn't really work. The Treaty of Versailles was a non-entity before Hitler came to power, and much of the gains he made afterwards were either inevitable (Saarland) or were not part of the treaty per se (Sudetenland). As early as 1938, Hitler was on the war path, the goal being to eliminate the Western Powers and then invade the USSR for Lebensraum.

Moreover, claiming the second is merely a continuation of the first ignores key differences. Japan, Italy, and Romania were members of the Axis, not the Allies; Fascism and Communism had not been major political concepts before the war; Germany's war aims, although expansionist, did not involve (much) mass genocide and ethnic cleansing. Moreover, this is a blatantly Eurocentric concept, in that it ignores Japan, China, and the Asian Theatre.

PMH Bell, Ruth Henig, and Michael Howard have all written on this subject, and have reached similar conclusions. To paraphrase Bell, it was the Depression that brought Hitler, and Hitler that brought the World War.

Would it be likely that WWI through WW2 would be seen sort of how we see the Hundred Years Wars?

As many others have suggested, it's really impossible to prove or disprove one way or the other. It's an exercise in counterfactual history.

It's perhaps a better question for political science, because that sort of stuff often involves the creation of models to explain historical facts.

My favorite model is the Long War theory, which was the crux of Philip K. Bobbit's The Shield of Achilles.

Bobbit's Long War theory is a fun explanation in and of itself, but it's not perfect. Basically the Long War is the idea that most of modern history has been defined by a series of conflicts centered around the dominant political theory. For most of human history, we have had nominally authoritarian governments (even if they weren't strongly centralized for most of history), usually autocracies taking the form of Monarchies.

This all changed with the "liberal revolution" that came about with the Age of Enlightenment, specifically with the philosophers writing about the social contract and the nature of governments (Rousseau in Du Contrat Social ou Principes du Droit Politique, Locke in his First and Second Treatise on Government, Hobbes in Leviathan, those sorts). Over time, more and more Imperial Monarchies fell, and started to get replaced, at first with Liberal-Democratic governments.

Here's where we get to your question. World War I, in this framework, is the death throes of the system of Imperial Monarchies. These entities (Ottoman Empire, Austria-Hungary, Imperial Germany, Czarist Russia) were all going to fall apart in the near future, and, as such, there was a competition between various political theories to fill the ideological vacuum following the collapse of the Imperial systems, just like there is always competition between various factions in a power vacuum following the collapse/removal of a government.

World War I, in this framework, was more or less Liberal-Democracy versus Imperial Monarchy, and Liberal-Democracy won, but it didn't finish the job. It took down the Imperial system, but it didn't replace it. In the wake of the collapse of Imperial Monarchy, you has the rise of Marxism/Communism, and the creation of Fascism.

Based on this line of thinking, another conflict was guaranteed. Fascism, Communism, and Liberal-Democratic Capitalism cannot peacefully coexist, since their systems of government and economy are so incongruent.

World War II happened because these systems were incompatible and at odds with each other, and the result of World War II was that Fascism was by and large destroyed as a major player for the future of the dominant political system.

This led to a bipolar system, with Liberal-Democratic Capitalism and Communism as the only two competitors left, which led directly to the Cold War. With the end of the Cold War and the conversion of former Communist economies to either Market systems or at the least hybridized economies, Communism is basically out of the picture.

This is where that whole idea of the Long War comes from: The Cold War is a result of World War II, which is a result of World War I, which in turn is tied to the Franco Prussian War, the Napoleonic Wars, the French Revolution, and the American Revolution. All of these wars had their obvious historical interconnections, but Bobbit believes that they are tied together far more closely, as part of a "super conflict" over two centuries long, in which various political systems fought for dominance on the world stage.

This concept is also very important to works such as Samuel P. Huntington's The Clash of Civilizations and the Remaking of World Order, and Y. Francis Fukuyama's The Last Man and the End of History.

So, that gives a framework that you can use if you choose to. The problem is, with all of these political science models, is that they are being approached with hindsight being 20/20, and a model is constructed to fit the historical realities. Personally I really like this theory and the various related theory (disclosure: Fukuyama is a family friend, so I am a bit biased about his works). I would suggest that give them a read if you are seriously interested, and form your own opinions.

In my opinion, this is a supposition that needs to be argued against. It seems obvious, link the Versailles Treaty with the rise of Nazism and boom! - WWI and WWII are the same conflict.

What this ignores is the singular influence of Adolf Hitler on world events. While it's impossible to say what would have happened without Hitler, the history of his rise and fall exactly parallels the prelude and ending of WWII. His actions as chancellor (then dictator) follow the script that he wrote in Mein Kampf. The chief aims of war for Hitler were leibensraum (living space) and racial purity. He then tried to carry out that plan.

A long analogy: I'm a physician, and one of the more interesting things that I've learned about is delusional mental illness. People who are "crazy" actually act rationally, it's just that their inputs are messed up. For example, if the CIA really was trying to control your brain with radio waves, wearing a tin foil hat may be a good defense. It's not the act that's irrational, it's the perception of reality.

In the same way, WWII cannot be analyzed without realizing that Hitler had specific goals (living space and racial purity). When asking why the Germans did or didn't do certain things, the reasoning becomes rational only when you consider Hitler's goals. In my opinion, Hitler was the singular actor that created WWII.