No it would not. Absolutely nothing would have brought the British into the Spanish Civil War.
I can't really agree on that one. A full-scale (attempted) German or Italian invasion of Spain (supporting the Nationalists), in direct breach of the Non-Intervention Pact which was intended to prevent that? To a certain degree, it's comparing apples and oranges to say that they wouldn't have gotten involved; direct military action on land by Britain would probably not even have resulted, just naval operations.
The backlash against dishonouring treaties is likely to be even larger than the backlash against giving up on Czechoslovakia in 1938, given the levels of popular support among the majority working class and intelligentsia for the Republic. Even if neither Baldwin nor Chamberlain gets involved themselves, it seems fairly likely that the National Government would have fallen apart and been reconstituted. Remember, also, that they had presented themselves as the government of honouring treaties and preserving international law in the last election, though with the example of Italy and Abyssinia being in mind in 1935.
It must also be noted that the basis of Chamberlain's 1938 actions was to 'avoid war', at least publicly; it does not square with his 'policy' to ignore it when another nation actively starts one. It seems a bit silly to assume that he'll steer an exactly identical course even with significantly different events occurring, especially with the likelihood of a two-front war (German armies in a conquered Spain and Germany itself in the oncoming war). Personally, I don't believe he would have been stupid enough to allow the National Government to fall down and trigger another election which could only go poorly for his own party. Reluctantly, to be certain, but in the case of a direct invasion of Spain, WWII is likely to start three years early.