  Most gravitational wave (GW) events observed by the LIGO and Virgo detectors
are consistent with mergers of binary black holes (BBHs) on quasi-circular
orbits. However, some events are also consistent with non-zero orbital
eccentricity, which can indicate that the binary formed via dynamical
interactions. Active GW search pipelines using quasi-circular waveform
templates are inefficient for detecting eccentric mergers. Also, analysing
eccentric GW signals with waveform models neglecting eccentricity can lead to
biases in the recovered parameters. We explore the detectability and
characterisation of eccentric signals when searches and analyses rely on
quasi-circular waveform models. We find that for a reference eccentric
population, the fraction of events having fitting factor (FF) $< 0.95$ can be
up to $\approx 2.2\%$ compared to $\approx 0.4\%$ for the baseline population.
This leads to the loss in signal recovery fraction for up to $6\%$ for
parameter space with non-negligible eccentricity ($e_{10} > 0.01$) and high
mass ratio ($q > 3$). We perform parameter estimation (PE) for non-spinning and
aligned-spin eccentric GW injections from BBHs with a total mass $M=35
M_\odot$, based on numerical relativity simulations and an EOB based
inspiral-merger-ringdown model (TEOBResumS). We recover these injections using
both quasi-circular and eccentric waveform models. For cases with $e_{20} \sim
0.1$, quasi-circular models fail to estimate chirp mass within the 90% credible
interval accurately. Further, for these low-mass injections, spin-induced
precession does not mimic eccentricity. For injections of $e_{20}\sim 0.1$, PE
conducted with an inspiral-only eccentric waveform model correctly
characterises the injected signal to within 90% confidence, and recovers the
injected eccentricities, suggesting that such models are sufficient for
characterisation of low-mass eccentric BBH. (abridged)
