It's almost impossible to ask "what might have been," but it seems almost entirely sure that the Army of Africa would have made it to mainland Spain at some point in the war, given the Republican fleet's incompetence (which led to Nationalist control of the Straits early in the war).

Let me refer you to pages 939-940 of Hugh Thomas' encyclopedic The Spanish Civil War (Revised and Enlarged Edition, 1977):

"Foreign intervention was, of course, of great importance in the war ... First, the supply of Junkers 52 by Germany in July 1926 helped Franco to lift the Army of Africa across the Straits of Gibraltar. To say simply that the nationalists would have lost the war had it not been for that begs too many questions. Some troops had been flown over before the Junkers arrived and, sooner or later, the rebels would have discovered the incompetence of the republican fleet; as indeed they did, when they gained control over the Straits at the end of September with the action of the Canarias. Still, the war would have taken a different course if the Army of Africa had not reached the mainland so fast. This help had a greater effect than the simultaneous purchase of aircraft by the republic from France, whatever the quantity or quality of the latter. The Junkers 52 (Iron Annie) cast its shadow over much of Europe between 1936 and 1945, never more than when it did so over the sea separating that continent from Africa in 1936."

If you believe the Army of Africa was vital, Adolf Hitler agrees with you. From Hitler's Table Talk, p. 687:

"Franco ought to erect a monument to the glory of the Junkers 52. It is this aircraft that the Spanish revolution has to thank for its victory."

But for all the praise about the airlift, it's often forgotten that much of the equipment of the army came by sea. On Aug. 5, the first convoy of ships ferried 3,000 men and their equipment from Morocco.

Why didn't the Republican navy interfere? Well, its leadership was incompetent and it didn't help that Germany had deployed the battleships Deutschland and Admiral Scheer to the area. Republican commanders believed (incorrectly, in hindsight) that an attack on the convoy might inspire the Germans to defend it, under the guise of "free navigation of the Straits."

With 500 men per day arriving by air and supplies landed by sea in Seville, the stage was set for a huge advance. In less than a month, the Army of Africa advanced 300 miles against militia resistance and was knocking at the gates of Madrid.

The Army of Africa was crucial to the way the war turned out, but the Nationalists might have found a way to win even without its intervention. In addition, the airlift -- while safer and quicker -- was not the only way to travel. The sea routes were wide open, and even if the airlift had not been available, those sea routes would have been used to move more men as well as equipment.