This is a question that verges into what-if territory, after all there is no "Earth B" with no world wars to test this hypothesis, but there were a number of latent fractures and contradictions of tsarist rule that made Russia very conducive to a revolution.
Russia had had a revolution just 12 years prior in 1905 that shook the tsarist edifice to its core. Although the tsarist state managed to weather the political storm, the 1905 Revolution was a sign of deep divisions. From a distance, it first appears that Russia's string of defeats against Japan caused a rise in antistate discontent, but the Russo-Japanese War was more of a pretext for the many groups and individuals disenchanted with Russia's existing political system. Nicholas II's concessions to more moderate political forces, which included a constitution and an elected assembly, bought the empire some time, but the post-1905 political order created new problems. In his biography of Stalin, Stephen Kotkin memorably termed the form of post-05 government "constitutional autocracy" and this turn of phrase accurately conveys the fundamental problems of Nicholas II's concessions. The Duma had little power and the franchise very limited, but Nicholas II had very little patience for even an anemic consultative body. The constitution enshrined elements of the tsar's rather broad and supreme power in Article One, which is itself a contradiction to how constitutions typically function as devices to delimit and define power. Moderate liberals were dissatisfied with these paltry concessions, as too were archconservatives who saw any concessions as dangerous. Thus the monarchy had only a very narrow base of support as i =t navigated the post-Revolutionary world. Radicals of various stripes were emboldened by the events of 1905, and the post-05 system provided very little in the way to incorporate these radicals into the system. In the interlude between 1905 and 1917, Russian politics grew more tense. Nicholas II's Prime Minister Stolypin, who tried to emulate Bismarck's "white revolutionary" politics (i.e. enacting social changes via archconservative means and justifications), found himself checked at various points by the entrenched power blocs within the tsarist system. Ethnic tensions within the empire were also threatening to bubble up. Pogroms against Jews in the Pale of Settlement had been a periodic affair since the assassination of the Tsar "Liberator" Alexander II, but the ones that occurred in the wake of 1905 were quite expansive. There was also tensions in central Asia and in the Western Provinces, as Russification efforts and colonial settlements created a backlash against Russian rule. Even Finland, which was one of the quiet backwaters of the Russian Empire, witnessed increasing conflict between the state and local elites who saw Russification and the growth of the imperial state as a violation of local privileges implicit in the tsar's personal union with the Grand Duchy. Assassinations and political violence was not uncommon. Stolypin died from an assassin's bullet, and there were widespread rumors at the time that the assassin, who was affiliated with various left-wing causes, was working in collusion with the archconservative right in the secret police to eliminate Stolypin. While these conspiracy theories are unproven, their existence at the time illustrates the incredibly lack of stability within the imperial system on the eve of war.
In a 2013 lecture at the LSE the historian Dominic Lieven notes that without the war, it would still have been possible for the Bolsheviks to seize power, but it is difficult to imagine a scenario in which they managed to keep it. Both Lenin and the Soviet state liked to play up the inevitability of Revolution, but Lieven's remark is a reminder that the situation was much more fluid in the run up to 1917. The tsarist state lacked many of the mechanisms to prevent a revolution in times of crisis, which provided any revolutionary group an opening. The Russian state had always suffered from a dearth of trained officials and bureaucrats, and this meant the autocratic state presented itself as a Goliath, its feet were made of clay. In 1905, extemporized security forces (the Black Hundreds) helped restore order, but these forces often exceeded their portfolio and visited violence against perceived enemies of national state. Nicholas II was thus trapped in a political cul-de-sac which there were very few ways to escape. Tsarist traditions and habits of rule prevented compromise with moderates to make the Romanovs more in line with other constitutional monarchs, but at the same time, neither could Nicholas II play the nationalist card and embrace Great Russian nationalism as this ethnic group made up only about 40% of the Empire's population.
While the war did not create the fractures within the tsarist system, they did sharpen preexisting social and political cleavages, and the scale of the war added new burdens as well, such as declining food production and infrastructural collapse. But the February and October Revolutions did not materialize out of thin air, and they often incorporated scripts and patterns of political protest that had occurred in 1905.
So while it is impossible to know the outcome of WWI-less Russia, the smart money would be to bet on some kind of revolution occurring as there were so many problems within the Empire and very few solutions to these problems that envisioned keeping the status quo.