Easily. Once Mussolini had alienated himself from Britain and France via his naval muscle flexing and pushing up against the Versailles status quo, aligning to Germany was the only way he'd get the diplomatic support and guranteed access to raw material (coal in particular) to pursue her ambitions comfortably
Going with your concept, and the majority of votes to date [the pro-Anschluss and Anti-COMINTERN side is winning the poll, 8:3] opens up the ability to do some interesting speculation on Spain itself, in comparative isolation.
Assuming my PoD from the OP:
PoD for there being no Spanish Civil War is the Spanish Centre-Right wins the mid 1930s elections.
But then proceeding and having European developments proceed basically as OTL, Anschluss, Munich, Poland, WWII.
I would guess that the default path for the alternate, center-right, non-dictatorial, non-Civil War devastated version of Spain would be neutral in the WWII in the ATL (as Spain was in WWI), only it would be more of a "true" neutral, like Switzerland and Sweden, without Franco's pro-Axis tilt.
It could also be much more prosperous and developed in the postwar era.
Does anybody disagree and think a no civil war, democratic Spain would be more likely to get drawn into WWII? Why so?
Of course, when would the next election in Spain be? If it's in 1940 and a popular front wins, what happens then? Especially if there is a Civil War at that time? Can Germany tolerate a center-left Spain that is neutral?
Also, how much is Soviet spending power reduced without the Spanish gold?