Alternative cementitious binders, based on industrial side streams, characterized by a low carbon footprint, are profitably proposed to partially replace Portland cement. Among these alternatives, alkali-activated materials have attracted attention as a promising cementitious binder. In this paper, the chemical stability of the matrix, in fiber-reinforced slag-based alkali-activated composites, was studied, in order to assess any possible effect of the presence of the reinforcement on the chemistry of polycondensation. For this purpose, organic fiber, cellulose, and an inorganic fiber, basalt, were chosen, showing a different behavior in the alkaline media that was used to activate the slag fine powders. The novelty of the paper is the study of consolidation by means of chemical measurements, more than from the mechanical point of view. The evaluation of the chemical behavior of the starting slag in NaOH, indeed, was preparatory to the understanding of the consolidation degree in the alkali-activated composites. The reactivity of alkali-activated composites was studied in water (integrity test, normed leaching test, pH and ionic conductivity), and acids (leaching in acetic acid and HCl attack). The presence of fibers does not favor nor hinder the geopolymerization process, even if an increase in the ionic conductivity in samples containing fibers leads to the hypothesis that samples with fibers are less consolidated, or that fiber dissolution contributes to the conductivity values. The amorphous fraction was enriched in silicon after HCl attack, but the structure was not completely dissolved, and the presence of an amorphous phase is confirmed (C–S–H gel). Basalt fibers partly dissolved in the alkaline environment, leading to the formation of a C–N–A–S–H gel surrounding the fibers. In contrast, cellulose fiber remained stable in both acidic and alkaline conditions.