In order to connect galaxy clusters to their progenitor protoclusters, we must constrain the star formation histories within their member galaxies and the timescale of virial collapse. In this paper we characterize the complex star-forming properties of a z = 2.5 protocluster in the COSMOS field using ALMA dust continuum and new Very Large Array CO (1-0) observations of two filaments associated with the structure, sometimes referred to as the "Hyperion" protocluster. We focus in particular on the protocluster "core," which has previously been suggested as the highest-redshift bona fide galaxy cluster traced by extended X-ray emission in a stacked Chandra/XMM image. We reanalyze these data and refute these claims, finding that at least 40% ± 17% of extended X-ray sources of similar luminosity and size at this redshift arise instead from inverse Compton scattering off recently extinguished radio galaxies rather than intracluster medium. Using ancillary COSMOS data, we also constrain the spectral energy distributions of the two filaments' eight constituent galaxies from the rest-frame UV to radio. We do not find evidence for enhanced star formation efficiency in the core and conclude that the constituent galaxies are already massive (M⋆ ≍ 1011 M⊙), with molecular gas reservoirs >1010 M⊙ that will be depleted within 200-400 Myr. Finally, we calculate the halo mass of the nested core at z = 2.5 and conclude that it will collapse into a cluster of (2-9) × 1014 M⊙, comparable to the size of the Coma Cluster at z = 0 and accounting for at least 50% of the total estimated halo mass of the extended "Hyperion" structure.