The only way to test this hypothesis objectively would be to divide humanity into 3 different planets. One planet would be in a constant state of warmongering, another would be full of hippies and another planet would be much like us. That would be our control group. For those not familiar with the term, a control group in an experiment or study does not receive treatment/intervention by the researchers so it can be used as a benchmark to measure how the other tested subjects do.
Since we are not able to perform such an experiment we will have to resort to speculation and rather extrapolate our conclusions based on some pivotal parts of humanity's development. For example, all great empires that ever existed had powerful militaristic dominion over their neighbors. Most of the developments in those civilisations occurred in times of war as a result of competition. Later on at times of peace those innovations were utilised in different ways. More or less, for the last 7500 years (aka the time upon which human civilisation has existed) war has been paving the way humanity moves forward.
Ancient Egypt ruled for 4000 years. It was through their ruthless medical experimentations on slaves that medicine got to be advanced and later on carried out by the Greeks. Architectural marvels like the pyramids, were enabled by the amassing of slaves as spoils of war. Through the manpower architects developed new concepts that wouldn't be possible otherwise.
The Roman Empire that lasted for 500 years developed our war necessity newspapers for getting the armies informed. Roads to have access to all possible venues and thus enabling control. Welfare, for supplying the conquered and those least ftunate in the Empire. In medicine, they have pioneered in innovations such as the cesarean section and field doctors, that performed surgeries in the battlefield. Due to their excellent written record, those techniques were followed much later during the Renaissance and the Enlightenment.
Recent examples would be aviation since it flourished between the 1930s and 1990s, a time where the world superpowers were competing to control the skies. Competition allowed funding for projects which otherwise would not have received a green light. Space exploration followed a very similar path. The cold war and the consequent space race enabled innovations like the satellite to take place after insane amounts of money poured into the military. Likewise, nuclear energy might not have been possible without the atrocities of the atomic age. Consider that famous people like Richard Feynman and Albert Einstein were on board with the nuclear bomb (even if they later regretted it). Undeniably much of the technology that exists today disposal is direct side effect of wartime innovation.
Other pieces of technology like radios, submarines and semiconductors were pivotal in human progress and they were all results in times of war as a way to have an edge over the enemy. Without transistors and semiconductors we wouldn't have developed computers. Alan Turing, the father of cryptography and for many computing was pushed immensely to find solutions decrypting military devices and this is how the allies ended up winning the war. Without the military the advancement towards this spectrum would be hindered and probably get slowed down.
To envision how unlikely the internet progress has been, Paul Robin Krugman, a distinguished keynesian economist who was awarded the Nobel price said: "By 2005 or so, it will become clear that the Internet's impact on the economy has been no greater than the fax machine's". This is to show that even after so many advancements in this technology very few people could envision the present we have today. Imagine how hard this was back in 1930's when computers were the size of a small living room. The first pivotal step only happened because of military advancement.
War challenges our species towards innovation because it creates new necessities. New problems emerge due to direct competition and new solutions are urged to be found asap because they are matter of survival. One is much more efficient in seeking food when hungry rather than when they are spoiled and well nourished.
The entire argument about war and innovation stems from another paradigm that all species go through. If the environment is challenging then the organism will adapt by changing its behaviour and qualities. If the environment is passive and unchanging the there is no need for radical evolutionary adaptations.
War is nothing more but an expression of conflict between two parties. It is a form of competition where the strongest prevails. We have similar competitions today in regards to many parts of our lives. Instead of spilling blood we rather define our victories with reputation and awards.
Many technological innovations happened in time of peace and then used in times of war.Surely, not all innovations are a result of war. Nonetheless, the world would be a totally different place if we were a peaceful species. Much of what we see today, much of what defines our life and current state of revolutionary development would not have existed for centuries if major wars did not take place.