  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 VLA 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 re-analyze
this data and refute these claims, finding that at least 40 $\pm$ 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 SEDs 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$_{\star} \approx 10^{11} M_{\odot}$), with molecular gas reservoirs
$>10^{10} M_{\odot}$ 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 $\times 10^{14} M_{\odot}$, 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.
