The increasing demand for sustainable construction materials has accelerated the development of alternative aggregate systems for pervious concrete. This study investigates the performance of fly ash-based pervious geopolymer concrete incorporating engineered synthetic aggregates manufactured from alkali-activated ground granulated blast furnace slag (GGBS). Class F fly ash with 5% silica fume was used as the geopolymer binder, activated by a sodium hydroxide to sodium silicate solution. Five mixtures were prepared by simultaneously varying the fly ash (15–35%) and coarse aggregate (80–60%) contents on a mass basis. The density, compressive strength, flexural strength, splitting tensile strength, and percolation rate of mixtures containing engineered synthetic aggregates were experimentally compared with corresponding natural aggregate mixtures. The synthetic aggregate mixtures exhibited lower dry densities (1519–1838 kg/m3) than the natural aggregate mixtures (1603–2110 kg/m3). Compressive strength increased from 1.05 to 12.00 MPa for synthetic aggregate mixtures and from 2.18 to 10.50 MPa for natural aggregate mixtures. At higher fly ash contents, synthetic aggregate mixtures achieved superior mechanical performance while maintaining higher percolation rates. Exploratory regression analysis yielded strong empirical correlations (R2 = 0.8236–0.9883), describing trends within the investigated dataset. The findings demonstrate the technical feasibility of using GGBS-based engineered synthetic aggregates as a sustainable alternative to natural coarse aggregates in pervious geopolymer concrete under laboratory conditions.