Using the observed rate of short-duration gamma-ray bursts (GRBs) it is possible to make predictions for the detectable rate of compact binary coalescences in gravitational-wave detectors. We show that the nondetection of mergers in the existing LIGO/Virgo data constrains the beaming angles and progenitor masses of gamma-ray bursts, although these limits are fully consistent with existing expectations. We make predictions for the rate of events in future networks of gravitational-wave observatories, finding that the first detection of a neutron-star-neutron-star binary coalescence associated with the progenitors of short GRBs is likely to happen within the first 16 months of observation, even in the case of only two observatories (e.g., LIGO-Hanford and LIGO-Livingston) operating at intermediate sensitivities (e.g., advanced LIGO design sensitivity, but without signal recycling mirrors), and assuming a conservative distribution of beaming angles (e.g., all GRBs beamed within θ(j) = 30°). Less conservative assumptions reduce the waiting time until first detection to a period of weeks to months, with an event detection rate of >/~10/yr. Alternatively, the compact binary coalescence model of short GRBs can be ruled out if a binary is not seen within the first two years of operation of a LIGO-Hanford, LIGO-Livingston, and Virgo network at advanced design sensitivity. We also demonstrate that the gravitational wave detection rate of GRB triggered sources (i.e., those seen first in gamma rays) is lower than the rate of untriggered events (i.e., those seen only in gravitational waves) if θ(j)≲30°, independent of the noise curve, network configuration, and observed GRB rate. The first detection in gravitational waves of a binary GRB progenitor is therefore unlikely to be associated with the observation of a GRB.