Not really! Here's Horkheimer in ~1937: https://criticaltheoryworkshop.com/wp-content/uploads/2018/03/horkheimer_traditional-and-critical-theory.pdf

(The translation is later, and some notes to later works were added, but the original is 1937 as documented here just above the section heading: https://plato.stanford.edu/entries/horkheimer/#TraCriTheSumDisEarPro)

This is pre-postmodernization, though you can find many seeds of it already in Traditional and Critical Theory.