When the “international brigades” showed up in Spain to fight for the communists, the government wanted to use them in the same way; the problem was that many were “war tourists” with no real military value. They were often persona non grata in their own countries, and briefly found a sense of purpose until the army showed up and quickly set the pace of the war: gradually pushing the leftists into smaller areas, almost never giving back any ground, while starving the leftists of food and supplies. Many were looking for the exit long before the war ended; they were simply a propaganda tool who lost their luster as the atrocities against civilians (especially Catholic clergy/religious) of the side they supported were exposed to the world.
No, the International brigades, though a mixed lot, were considered to be more effective units than the usual Republican army unit, or a union militia. They were explicitly communist units organized by national communist party organizations, with commissars and all. They were generally used as an assault or counterattack force, under Communist generals, at the bloodbaths of Madrid (Especially at the Casa del Campo and Ciudad Universitaria, I have walked the ground there), Jarama, Brunete, Belchite, the Ebro, etc. and etc. They were very busy, and casualties were so heavy that most of them eventually had mostly Spanish replacements.