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The Reign in Spain didn't mainly have any planes.What did Spain have at this point, Air Force...
Likely Gibraltar would been a slug fest like Malta but it would not have fallen.
However, with Gibraltar taken, Malta would surely have been neutralized. The axis would even see no need to actually occupy it. And with Malta out ... the supplies get through to the Afrikakorps. As El Alamein was a close fought deal, it is very likely that the Suez would have been taken. Once the Suez, no more ships can supply the troops and Navy.one plus for the Axis, constant pressure on Gibraltar. Whether that pressure would have really affected anything that the Allies were doing... They had Malta surrounded too and that failed in the end. Germany being allowed to operate in Spain would be a plus for them. But it might just spread them out even thinner than they already were once Russia was invaded. Hitler had a habit of not wanting to wait before he started the next campaign. Likely Gibraltar would been a slug fest like Malta but it would not have fallen.
Also today I was reading another book "Mussolini and the origins of second world war". There is a reference to Guderian urging Hitler to delay French surrender and to allow him two Panzerdivisions to take through Spain, take Gibraltar and conquer French North Africa before peace negotiations. So, Guderian did not even consider it a problem marching through Spain. He was probably right. Franco would never have opposed it, he would have stuck to some formal protests.