We present the first comprehensive search for submillimeter and radio emission from the host galaxies of twenty well-localized gamma-ray bursts (GRBs). With the exception of a single source, all observations were undertaken months to years after the GRB explosions to ensure negligible contamination from the afterglows. We detect the host galaxy of GRB 000418 in both the sub-mm and radio, and the host galaxy of GRB 000210 only in the sub-mm. These observations, in conjunction with the previous detections of the host galaxies of GRB 980703 and GRB 010222, indicate that about 20% of GRB host galaxies are ultra-luminous and have star formation rates of about 500 M_sun/yr. As an ensemble, the non-detected hosts have a star formation rate of about 100 M_sun/yr (5-sigma) based on their radio emission. The detected and ensemble star formation rates exceed the optically values by an order of magnitude, indicating significant dust obscuration. In the same vein, the ratio of bolometric dust luminosity to UV luminosity for the hosts detected in the sub-mm and radio ranges from 20-800, and follows the known trend of increasing obscuration with increasing bolometric luminosity. We also show that, both as a sample and individually, the GRB host galaxies have bluer R-K colors as compared with galaxies selected in the sub-mm in the same redshift range. This possibly indicates that the stellar populations in the GRB hosts are on average younger, supporting the massive stellar progenitor scenario for GRBs, but it is also possible that GRB hosts are on average less dusty.
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