It wouldn't just be the cheap Tungsten and various other metals in the Iberian peninsula, but also denying the Brits access to the Mediterranean via Gibraltar, a naval base there, and extending Axis naval abilities quite a ways into the Atlantic.
On balance the Brits arguably have their blockade made easier in some ways while perhaps also having a more worried US public while the Axis has to feed, fuel, and supply Iberia with everything it needs to survive. Plus they get the Azores, which, while not yet having enough CC long range aircraft to really exploit it, can at least use it as a naval base in the mid-Atlantic.
So the ticking clock on the Axis is moving more quickly and louder the question is can they exploit the gains to make a decisive impact on the war before the burdens of their new ally decisively outweigh any benefits. Assuming not the likely the battle of the Atlantic can be won sooner than May 1943 and the Allies have to invade Spain in late 1942/early 1943 rather than North Africa or France. It would be highly interesting to know what Vichy France would do in this case given at least the delayed invasion of North Africa. Plus would the Axis abandon Libya if they have to heavily invest in the Spanish front? Much would of course depend on whether or not Barbarossa happens ITTL.
Interesting question. Lot of variables here so lets start with the easy stuff.
- Have to assume the invasion of Soviet Union still happens, or we have an Axis win via a butterfly. Or at least very, very slow Anglo-American win.
- Have to assume Germans don't divert so many forces that it is a disaster in attacking Russia in 1941. Or frees up enough Axis forces for a win in the east.
- As to USA invasion plans, my readings indicated that the USA always planned to attack on Southern most flank of Axis in Africa. For example, there were discussion at high levels that if the Vichy were to be actively Axis, the invasion might well occur in West Africa. Bringing Spain into the war does not shift the invasion north, but if it is shifted, it is shifted, the shift is south. The basic military strategy for amphibious operations is to land in a weakly defended area, organize, the attack with good supplies.
- The tungsten is interesting. I think this is a big advantage for the Axis, but I can't easily quantify. I do think Portugal will tend to fall if Spain enters the war for any reason.
Now to the fun stuff for me. Can this win the war for the Axis instead of merely cause the Americans to have to grind more to get to Germany? While I think owning the western Med helps the Italians a lot in Africa, I don't think it will allow the Italians to take the Suez much less exploit the Red Sea. As the Axis advance, the supply situation keeps getting easier for the UK and harder for the Italians. And even taking the Suez just means the UK has to bottle up the Red Sea and hold in the Sinai which can still be supplied. So I think we just see attrition here. I don't happen to have the North African campaign memorized on the Order of Battle, but I think the net effect from OTL is some flow of Nazi resources from North Africa to the Russian campaign, and the net flow is in the order of magnitude of regiments and squadrons. Useful, but not decisive in any given month.
So then we get to the Battle of the Atlantic. Any surface German naval forces can be based now outside of easy bomber range for the UK. And in theory the Italian Navy can come out in mass for battle, but I don't think this is likely. The UK will keep a stronger force to counter, and if push comes to shove, I think the USA will informally commit naval resources. Our plans called for occupation of islands to prevent the Nazi from taking over, so it is not really a stretch to see USA naval forces in the Azores as a part of this plan. Or land units for that matter.
So then we get to the naval war. Presumably, the Germans and Italians will base medium bombers and naval aviation in Spain and Portugal. These will cause slightly increased losses and force the Allies to move shipping farther west. The limited shipping that goes to the South Atlantic. The detour is measured in days, maybe a week each way, so the Allies may lose a few % cargo capacity. This does not seem like a war winner at first blush since it would seem to do things like delay the 8th Air Force becoming active by a few weeks to a few months.
The biggest direct impact I can see is the U-boats moving South which will force the UK to form convoys farther south and strain destroyer resources. This would take a good bit of modeling to get right, but it does not seem like a war winner. My guess, just a guess, is we again see a few % loss of shipping to the UK.
So when I add this up, I don't see a win for the Axis on the first pass. We see single digit decreases in shipping, few more divisions in Russia, few more squadrons in Russia, bombing offensive being weeks behind OTL. Italy stays in war til end cause American forces just can't get there fast enough. Looks like post war Soviet wank really. Now if the butterflies add up enough and in series, then maybe. But I have to be a bit of an optimist for the Nazi. You have to have Spain not turn into a net resource drain for the Heer. I then have to have things such as the equivalent of OTL Afrika Corp added to Barbarossa. Then this extra Panzer Corp or Panzer Army has to accomplish something important (Leningrad falls, much better Moscow result, holding farther east in South in 1941 so 1942 operations go better). I then have to believe the Italians apply equal or greater pressure to the British in Egypt to keep the UK busy. Then I need 1942 in the east to go much better due to weaker Soviet forces than OTL and some additional gains by Germans in 1941. And I need absolute great performance in 1942 by Heer. Then the Heer can knock out the Soviets before the USA enters the war with large number of forces in mid 1943.
So to me at least, I think the odds of this action winning the war for the Axis is will under 5% but probably over 1%. Interesting to discuss but quite a long shot.