ABSTRACT We present Atacama Large Millimeter/submillimeter Array (ALMA) 870 m (345 GHz) data for 49 high-redshift (0.47 < z < 2.85), luminous ( ) radio-powerful active galactic nuclei (AGNs), obtained to constrain cool dust emission from starbursts concurrent with highly obscured radiative-mode black hole (BH) accretion in massive galaxies that possess a small radio jet. The sample was selected from the Wide-field Infrared Survey Explorer with extremely steep (red) mid-infrared colors and with compact radio emission from NVSS/FIRST. Twenty-six sources are detected at 870 m, and we find that the sample has large mid- to far-infrared luminosity ratios, consistent with a dominant and highly obscured quasar. The rest-frame 3 GHz radio powers are and all sources are radio-intermediate or radio-loud. BH mass estimates are 7.7 < log(MBH/M ) < 10.2. The rest-frame 1-5 m spectral energy distributions are very similar to the "Hot DOGs" (hot dust-obscured galaxies), and steeper (redder) than almost any other known extragalactic sources. ISM masses estimated for the ALMA-detected sources are 9.9 < log (MISM/M ) < 11.75 assuming a dust temperature of 30 K. The cool dust emission is consistent with star formation rates reaching several thousand M yr−1, depending on the assumed dust temperature, but we cannot rule out the alternative that the AGN powers all the emission in some cases. Our best constrained source has radiative transfer solutions with approximately equal contributions from an obscured AGN and a young (10-15 Myr) compact starburst.