An interesting idea. The Spaniards would go into it for Gibraltar, most likely, and the probability that a German-Italian-Spanish operation there might succeed is quite high, if it was planned correctly. With Gibraltar removed, it would make things - as you have already said - far easier in the Mediterranean. Would Rommel be successful in capturing Egypt?

Also, what would Portugal do?

As another thought, how about the British landing in Portugal, recreating the scenario from the Napoleonic Wars.

But there might also have been a drawback - Spain would certainly have wanted up to date German equipment and this could have been a drain that might have proved fatal on the Eastern Front (where Spain would be next to no help at all).

Spanish Navy - I remember looking this up once. From a very clouded memory I seem to remember it being a lot smaller than the Italian and even worse in quality. I wouldn't count on it to change things in the Atlantic.

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„Solange man nicht mit dem Kopf unterm Arm rumläuft geht es doch noch!" Erwin Rommel