Quicker victory for the Nationalists. Without material support from the Soviets, the Republican war effort would have ran out of guns. People always make out that the Soviets were the main reason the war fell apart for the Left Front and that may have some credence if you look at Catelonia alone through Orwell-tinted glasses but in Madrid it was the arrival of the international brigades, often armed and supplied by the Soviets, that was all that was in between a fascist takeover. The Soviets had the Republicans' only tank brigade, their only bomber wings and thousands of artillery and small arms supplied throughout the war. While the Soviets were arming the Republicans, the British and French were actively preventing arms shipments.Hitler goes to art school. Germany falls into civil war, distracting the Soviet union from Spain. Assuming there is still a civil war how would play out without the infighting caused by the soviet politicking, and no German support for the Nationalists.
Can their maybe be an anarchist dominance in Spain after the war?
Stalemate yes. Victory, not necessarily so. The Anarchist militas were fine at defending their homes and factories, but lacked any of the disciplines to properly attack. Their assaults on Army barracks etc were very heavy in casualties as they substituted bravery for tactical sense.
EDIT: And if the Italian's are tied up in Germany, then I'd wager that the French would certainly be willing to help out the Republicans. Which makes it pretty much certain that they'll triumph fairly quickly.
This actually may be the case... however this has little to do with ideology, and much more to do with lacking experience in previous conflicts, along with a completely new military structure.
Additionally, the Nationalist faction really wasn't any better at first.
It probably helped that the Nationalists had actual generals who had experience in combat.