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.
They were used as cannon fodder (worth far less than Republican regulars), and they often had no military background - especially those from the US (some ageing European leftists had seen action in WWI). The leftist government was quite willing to send them home when it felt the Nationalists might do the same with their Italian troops (which they didn’t); they were paper tigers who took losses but were ineffective against Franco’s regulars. Their real contribution was as propaganda tools (to give the appearance of a real international effort), but their numbers were small and they were often from countries that didn’t want them anyway.