Well considering the development of armoured cars was already well underway before the First World War began, it is highly likely that the natural progression would have eventually led to the development of the tank though not for many years down the track due to the limitations of internal combustion engines. What we probably would not see is the tank take the form that we saw it take in WW1. The development of the landship and its subsequent design elements were a direct result of the conditions present on the Western Front. The need to cross boggy ground, trenches and crush barbed wire led to the adoption of caterpillar tracks and the angled and elongated overall shape. Without the need to overcome these conditions, we would probably have seen the tank designed with large wheels, probably tyres as well and would probably have looked more like a larger and more heavily armed armoured car. Your question also hinges on the assumption that there still would have been a Second World War which is incorrect due to WW2 being a direct consequence on WW1.

As for how important the development of the tank was, opinions vary, some historians support the notion that the tank was instrumental in overcoming German defences while others put it down to a mixture of technologies and tactics. Personally, I support the second view. By the time the tank was capable of playing a decisive part in the war, artillery technology had reached the point where German defences could be successfully neutralised to the point that the infantry could secure their objectives. What the tank did bring to the battlefield was much needed mobile and local firepower support. At the Battle of Hamel in 1918, the artillery virtually wiped out any German resistance. When the infantry advanced, they did come under fire from surviving German positions. Due to the limitations of communications, artillery was unable to be quickly brought to bear on the positions. The presence of the accompanying tanks allowed the attacking Australians to deal with these positions without suffering excessive casualties attempting to rush and neutralise German machine guns. Tanks were also highly successful in their use as carriers. A single tank could carry the equivalent of what 80 men were required to carry to the front.

We get a bit of a clue to the answer from actual events. For although only Britain an France developed tanks in the Great War (no, I don't count the dozen or so A7Vs, which were virtually improvisations), the British set about forgetting what they'd learned after the war, ever-narrowing budgets so her tank force was little more than an experimental resource.

The lessons of 1918 were seen in the 'Medium' series, but these were soon focussed on overcoming technical issues such as track design as the more combat-related aspects of design withered. The most successful inter-war tank was the 'Vickers Six Ton', designed in 1928, and resembling the modern tank with a rotating turret.

So, the question becomes whether the lessons that were taken out of the First World War and applied to tanks: principally rotating turrets and general layout (although only one 1918 tank had a rotating turret its advantage was realised), would not have been realised in peacetime.

My feeling is the tanks of 1939 would have looked very much how they did anyway. What was learnt in WW1 was either forgotten, or had been replaced by an entirely new set of technical challenges- and often economic constraints- such that an engineer designing a tank in the late 1930s would have gained little from knowledge of the Mark V or Whippet.

Many of the tanks actually fielded in 1939 were either almost useless (the fleets of 'tankettes') or flawed (one man turrets, underpowered engines, unreliable track arrangements). Tank development was very rapid in all countries as new lessons were absorbed. And of course tactically they were being used in completely new ways.