The Republican government was a coalition government ranging from the centre all the way to the furthest (democratic) left, and continued to be this broad coalition for much of the civil war. While the coalition did turn more to the left during the course of the civil war, this seems to be more because of effects from the international system, where France and UK only allowed volunteers to go (And sometimes blocked support to the Republicans), and these volunteers were often centre-left, and because USSR provided more direct support.
To say that the Republicans were socialists, however, is wrong. The popular front was incredibly diverse, ranging from the nationalist movements of the Basque and Catalonian regions, the centrist republicans, socialdemocrats, communists and anarchists. To predict how this group would go had they won the civil war, seems to be incredibly difficult.
However, I do think we can make a reasonable guess that has gameplay effects.
- The Spanish Republicans did seem to go towards the 'side' (In ideological/geopolitical terms) that provided the largest and most consistent support. This may have been simple correlation, without any causation, but in gameplay terms it can be useful. If it's implemented so that support in civil wars will increase the power of your own faction in that country if they win, civil wars can become interesting even for people who are nominally on the same side.
Imagine if a multiplayer game with UK, Germany and USSR players. They have to respond to the Spanish Civil War, with Germany and USSR going the historical route with direct support.
The UK player, after a while, sees that the communists on the Republican side have gained enough power to make Spain communist after the civil war, will have to decide whether that can be allowed or, if not, what to do about it. The UK could then supply the Republicans in an effort to reverse the effects of the Soviet support.
One can dream...