In general you're right that their role was greatly overblown by foreign and Republican media, in order to create the impression of a worldwide popular mobilization standing shoulder to shoulder with the Spanish Republic, which clearly was not the case.
It's not fair to say that the International Brigades suffered, in an absolute sense, from lack of military training. Its volunteers certainly included young and idealistic men --unemployed or intellectual-- who had missed out on the world war, but also many veterans of the Great War and the many local entanglements that had resulted from it (Great War veterans like Kleber, Tito and Marty; Irish volunteers who had experience in the Irish Independence and Civil Wars; Austrian and German activists with experience in those countries' political paramilitaries, etc.). That's not a negligible factor, given that neither the Spanish military nor the civilian population had ever experienced anything resembling the total war of 1914-18 (with the possible exception of the October 194 rising), so men who could be trusted to hold the line under the commotion of shellfire was not insignificant.
Rather, the challenge to their effectiveness was one of discipline, of forging an effective force from a heterogeneous base: Volunteers from dozens of different countries, with different expectations, military traditions, languages, political families. So for example, you have the Irish volunteers being assigned to the American after protesting being placed under British officers; you have British liberals such as Orwell baulking at the idea of communist discipline; you have American troops mutinying over the question of deployment and imposed officers.
As regards their military usefulness. Although the Brigades participated in several engagements between 1936 and their dissolution in 1938, their role was not game-changing. However, nor were they superfluous to the war effort for one major reason: they arrived into Madrid on the fourth day of the capital's siege, providing the city with its sole effective full strength military force. At a moment when the regular army and armed police had been disrupted by defections to the rebels, the lack of dependable defenders had led the Republican government to flee the city. Now again, that's not to say that the Brigades were the only fighters; they were three thousand out of forty thousand --but many of the Spanish defenders were untested recruits in political militias, accustomed to street brawls but untrained in modern warfare. So in the very early days of the war, the International Brigades tipped the scales in favour of the defenders of Madrid at a crucial moment when the city was badly in need of trained fighters. By keeping the rebel troops out of the capital (at a horrendous cost in lives), the International Brigades were of both a practical and symbolic importance to the Republic at its moment of greatest confusion and disorganization.
It wouldn't be before the end of 1936 that the ragtag political militias, greater on enthusiasm than expertise, began to be formed into a cohesive Republican army. In the weeks after the Brigades' initial arrival, the Republic rebuilt an army from the ground up, and the International Brigades were increasingly not needed and became a diplomatic liability, withdrawn from combat and eventually sent home. Even where they participated in combat in 1937 and 1938, they were now a regular part of the Republic's Popular Army: by 1937 60% of their members were Spaniards.
In summary: yes their role is exaggerated, both in terms of their numbers and effectiveness. But nor were they superfluous, offering a valuable military and morale-boosting resource in the critical month of October 1936.
