Sanjurjo died 2-3 days after the Civil War started, trying to get back to Spain from his exile in Portugal. He was one of the key conspirators in the failed coup that started the Civil War, but you can’t really call him “the Leader of the Nationalist forces” for longer than a few days anyway.
As Danhagen points out that would have left the Canary Islands sitting ducks for an Allied takeover, giving the Allies a island fortress base to eventually attack Spain, a south route refueling depot to fly the Atlantic, block trade routes, etc. Plus, then Spain would need think about to maintain a bigger standing army and build up their arms to defend against a future invasion. Depends whether Gibraltar for Canaries was a good trade.
I think you can. He had been the person who started the movement, recruited everyone, and planned out the uprising. The fact that he died right at the beginning up the uprising doesn’t negate all the work that went into getting to that point.
Thinking more about the results of Franco joining the war c1943.
Yeah, Gibraltar would be dead meat. But conversely this would have given the Allies a great excuse to land in Spain in order to attack into France. No way could Franco, even with Hitler’s help, done a very good job in defending that coastline.
And once in Spain, then the old rivalry issues arise. The Allies start arming anti-Falangists, etc.
Also, Portugal would be a problem. While nominally a Fascist state at the time, the rivalry with Spain was intense and it was fairly friendly for a long time with the UK. Maybe the Allies could have attacked via Portugal. No need for an assault landing.
Retaking Gibraltar from Portugal would be a breeze.
OTOH, c1940, no way could the UK done anything like this. Once the Russians entered the war, I don’t think they could have provided much support against Spain, despite their remaining supporters there. But I’m sure the Leftists would have taken US and British weapons just as much as Stalin did.
In general, I keep coming back to the issue of internal enemies that had to be a big part of Franco’s thinking.