  A new family of restricted post-Newtonian-accurate waveforms, termed TaylorEt
approximants, was recently proposed for searching gravitational wave (GW)
signals from inspiraling non-spinning compact binaries having arbitrary
mass-ratios. We perform detailed fitting factor (FF) studies to probe if the
TaylorEt (3.5PN) signals for non-spinning comparable mass compact binaries can
be effectually and faithfully searched with TaylorT1, TaylorT4, and TaylorF2
(3.5PN) templates in LIGO, Advanced LIGO, and Virgo interferometers. We observe
that a good fraction of the templates, which by choice are from TaylorT1,
TaylorT4, and TaylorF2 (3.5PN) families, have FF <~ 0.97 and substantial biases
for the estimated total-mass against the fiducial TaylorEt (3.5PN) signals for
equal-mass systems. Both these observations can bear on the detectability of a
signal. TaylorEt (3.5PN) signals with mass-ratios of a third or a quarter yield
high FFs against those same template banks, but at the expense of inviting
large systematic errors in the estimated values of their total mass and
symmetric mass-ratio. In general, the aforementioned templates are found to be
increasingly {\it unfaithful} with respect to a TaylorEt signal as one
increases the total mass of the inspiraling system. We also observe that the
amount of bias in the estimated mass varies with the (noise power spectral
density of the) detector. This can be of some concern for multi-detector
searches, which check for consistency in the estimated masses of concurrent
triggers in their data. (Abridged)
