The Allies were incredibly concerned about the prospect of Franco's Spain joining the Axis, and in some ways, those concerns can, at least partially, be seen to have shaped the way the rest of the war unfolded.

This is mainly evident in the planning of Operation Torch, the first major inter-allied operation in the Western theatre, which aimed to land in Algeria and Morocco and push east into Tunisia, thereby pincering Axis forces in Africa, and moving towards securing Allied supply lines through the Mediterranean. However, in planning these landings, although the British Chiefs of Staff pushed for landings as far east as possible, namely at Bone near the Tunisian border, the Americans Joint Chiefs insisted on at least one Atlantic landing, at Casablanca, the main reason for which was the prospect of Spanish intervention, which could cut off Allied communications through the Straits of Gibraltar. By landing in Casablanca and then skirting round Spanish North Africa, the Allies would have a continuous supply route from the Atlantic, and would also be in a stronger position to counter any potentially hostile moves from Spanish forces.

The long term consequences of these strategic choices were arguably massive; by landing further west, the Allies could not reach Tunis in time to prevent the landing of further Axis troops, under Walter Nehring, which blunted the offensive of General Anderson's scratch force, and prolonged the campaign for up to another six months. The resulting Tunisian campaign would see American troops receiving some of their first ground experience against the Germans, rapid advancements in Allied warfighting (in particular how to command multinational forces), and would culminate with a haul of Axis PoWs on a magnitude larger than Stalingrad (according to some). The prolonged nature of the Tunisian Campaign would also see the Allies adopt the 'Mediterranean Strategy', attacking the 'soft underbelly' of Italy imagined by Churchill, thus shaping Allied strategic decisions in the ongoing war; the JCoS had originally championed a 1943 invasion of France codenamed Roundup (an even more ambitious 1942 plan of the same variety had also been created called 'Sledgehammer'), but the ongoing demands of Tunisia, particularly on Allied shipping, and the need to maintain a second front, persuaded the Allies into Sicily, and then Italy. As such, the part played by the threat of Spanish intervention, and its consequent impact of Allied strategy, can arguably be seen to have shaped the course of the war itself.

As for projections, I'm not particularly familiar with intimate detail, but some of the Cabinet files regarding Spanish intervention can be found in CAB 80, in the National Archives in Kew. CAB 79/57 also contains files particularly pertaining to Spanish reactions to Operation Torch, and Allied counterplanning in case of Spanish hostility.

Sources

George F. Howe, Northwest Africa: Seizing the Initiative in the West (Washington D.C.: Office of the Chief of Military History, 1957)

Matthew Jones, Britain, the United States and the Mediterranean War, 1942-44 (London: Macmillan, 1996)

Kenneth Macksey, Crucible of Power: The Fight for Tunisia, 1942-1943 (London: Hutchinson & Co., 1969)

Major General I.S.O. Playfair, Official History of the Second World War, The Mediterranean and Middle East, vol.4: The Destruction of the Axis Forces in Africa (HMSO: 1966)