There was a fear in London and Washington that he would do just that because of his isolation; but because Fascism and Communism are ideologically opposite, that's why he opposed them. Not to mention, the USSR supported the Republicans during the Spanish Civil War, whereas Italy and Nazi Germany supported him. Him and Salazar (Portugal's Fascist leader) even sent an army division to aid in Germany's Invasion of the Soviet Union. So him siding with Communism defies everything he believes in.
I think if he sides with Communism, Anglo-French agents are given the green light by Washington to remove him and/or overthrow the Fascist regime in Spain.