One of the open questions following the discovery of GW170817 is whether neutron star mergers are the only astrophysical sites capable of producing \(r\)-process elements. Simulations have shown that 0.01-0.1M\(_\odot\) of \(r\)-process material could be generated in the outflows originating from the accretion disk surrounding the rapidly rotating black hole that forms as a remnant to both neutron star mergers and collapsing massive stars associated with long-duration gamma-ray bursts (collapsars). The hallmark signature of \(r\)-process nucleosynthesis in the binary neutron star merger GW170817 was its long-lasting near-infrared emission, thus motivating a systematic photometric study of the light curves of broadlined stripped-envelope (Ic-BL) supernovae (SNe) associated with collapsars. We present the first systematic study of 25 SNe Ic-BL -- including 18 observed with the Zwicky Transient Facility and 7 from the literature -- in the optical/near-infrared bands to determine what quantity of \(r\)-process material, if any, is synthesized in these explosions. Using semi-analytic models designed to account for \(r\)-process production in SNe Ic-BL, we perform light curve fitting to derive constraints on the \(r\)-process mass for these SNe. We also perform independent light curve fits to models without \(r\)-process. We find that the \(r\)-process-free models are a better fit to the light curves of the objects in our sample. Thus we find no compelling evidence of \(r\)-process enrichment in any of our objects. Further high-cadence infrared photometric studies and nebular spectroscopic analysis would be sensitive to smaller quantities of \(r\)-process ejecta mass or indicate whether all collapsars are completely devoid of \(r\)-process nucleosynthesis.