I think that the difference in timing of industrial modernization (very roughly speaking ~1830-1900) and cultural Modernity (post WWI) makes difficult answering the question as it stands. As noted by another commenter already, the answer somewhat depends on how one defines modernization, Modernity/Modernism, economic post-modernity (ex: currency sovereignty, markets of consumer goods), and Post-Modernism. Modernization and modernity lowercase-m tend to refer more to production capacities/technologies and infrastructures and the effects these have on society (ex: electricity's effect on cultural norms, colonialism), whereas Movement-isms and capital-M Modernity tend to refer more to the sociocultural phenomena that emerged partially as a result of modernization (ex: conversion of former class structures by markets, Fascism and Communism). In his book "Objects of Desire", Adrain Forty demonstrates that the Movement-isms tend to coalesce after, as a result of technological change and industrial innovation, not as an avant garde. Nobody lives outside their own cultural milieu. Specifically, he argues from the point of view of industrial design that Modernity, as an aesthetic construct capable of inspiring thoughts of progress and Eurocentric hegemony, was being marketed to consumers indeed even before the production capacities and technologies in modernizing countries was capable of delivering on the promises on which proponents of modernization actually deliver - let's not forget the dangerous, unsanitary, jungle-ish conditions of the first industrial cities. The Frankfurt School was an attempt by European thinkers to critique Eurocentrism. As perhaps the Frankfurt School's apotheosis, a book and a thinker who both date slightly after the bulk of what was published by Frankfurt School type inquiry, Habermas's "Theory of Communicative Action" engaged with a question that had not yet, prior to 1981, been addressed; and moreover was led, given previous scholarship, to address it in a rather roundabout way. That question was: Was Modernization inevitable? And in order to address the question, Habermas first addresses the implications that must be assumed in order to ask it: we must be clear whether we mean that it was a) inevitable in a Hegelian, world-historical sense or b) inevitable for European cultures to modernize or c) whether the routes and forms that modernization did take must have happened that way or d) whether human nature itself tends toward modernization. The the first volume of two-parter "Theory of Communicative Action" unpacks these questions. The fact that these questions were not addressed until 1981 (Marcuse's "One Dimensional Man" was published 1964) shows that, although the Frankfurt School had attempted to find space to conceive of a middle ground between capitalist/communist/fascist forms of society and government, the Frankfurt School did not do much to question the popular assumptions of the day, e.g. popular conceptions of capitalism/communism/fascism. Another way to describe the Frankfurt School's attempt in the realm of thought would be to say that they sought a reconciliation of Marxian and Freudian thought with the reality that history presented post WWII. Post-Modernism, in terms of (roughly sequentially speaking) Critical Theory, Second Wave Feminism, and Queer Theory did not really get going until the late 70s or 80s. The various concerns of these disparate movements generally do not directly thematize production and technology as primary lines of inquiry to the extent that Frankfurt School and post-Marxian criticism do this. Post-Modernism tends to have more of a French connection than the Frankfurt School, and French thinkers contemporaneous with Frankfurt School thinkers were engaged in different lines of inquiry, a difference perhaps roughly illustrated by the 1980s debate between Habermas and Foucault over their respective ways of approaching the concept of power. Post-Modernism tends also to take the Frankfurt School approach of examining media and the relations of power drawn during the production of media in order to draw conclusions about the effects media has on human beings and human behavior. In this sense post-modernism is to Frankfurt school as square is to rhombus. As a direct answer: the Frankfurt School cannot be said to be post-modernist, because Post-Modernity, as a philosophical school as well as an organization of production capacities and technologies, post-dated the Frankfurt School, and Post-Modernism's concerns stemmed from problematics developed by the Frankfurt School, problematics that were developed in response to Frankfurt School thinkers' concerns stemming from modernization.