  The Fermi Gamma-ray Burst Monitor (GBM) is currently the most prolific
detector of Gamma-Ray Bursts (GRBs). Recently the detection rate of short GRBs
(SGRBs) has been dramatically increased through the use of ground-based
searches that analyze GBM continuous time tagged event (CTTE) data. Here we
examine the efficiency of a method developed to search CTTE data for
sub-threshold transient events in temporal coincidence with LIGO/Virgo compact
binary coalescence triggers. This targeted search operates by coherently
combining data from all 14 GBM detectors by taking into account the complex
spatial and energy dependent response of each detector. We use the method to
examine a sample of SGRBs that were independently detected by the Burst Alert
Telescope on board the Neil Gehrels Swift Observatory, but which were too
intrinsically weak or viewed with unfavorable instrument geometry to initiate
an on-board trigger of GBM. We find that the search can successfully recover a
majority of the BAT detected sample in the CTTE data. We show that the targeted
search of CTTE data will be crucial in increasing the GBM sensitivity, and
hence the gamma-ray horizon, to weak events such as GRB 170817A. We also
examine the properties of the GBM signal possibly associated with the LIGO
detection of GW150914 and show that it is consistent with the observed
properties of other sub-threshold SGRBs in our sample. We find that the
targeted search is capable of recovering true astrophysical signals as weak as
the signal associated with GW150914 in the untriggered data.
