  Gravitational-wave observations provide the unique opportunity of studying
black hole formation channels and histories -- but only if we can identify
their origin. One such formation mechanism is the dynamical synthesis of black
hole binaries in dense stellar systems. Given the expected isotropic
distribution of component spins of binary black hole in gas-free dynamical
environments, the presence of anti-aligned or in-plane spins with respect to
the orbital angular momentum is considered a tell-tale sign of a merger's
dynamical origin. Even in the scenario where birth spins of black holes are
low, hierarchical mergers attain large component spins due to the orbital
angular momentum of the prior merger. However, measuring such spin
configurations is difficult. Here, we quantify the efficacy of the spin
parameters encoding aligned-spin ($\chi_{\rm eff}$) and in-plane spin
($\chi_{\rm p}$) at classifying such hierarchical systems. Using Monte Carlo
cluster simulations to generate a realistic distribution of hierarchical merger
parameters from globular clusters, we can infer mergers' $\chi_{\rm eff}$ and
$\chi_{rm p}$. The cluster populations are simulated using Advanced LIGO-Virgo
sensitivity during the detector network's third observing period and
projections for design sensitivity. Using a "likelihood-ratio"-based statistic,
we find that $\sim2\%$ of the recovered population by the current
gravitational-wave detector network has a statistically significant $\chi_{\rm
p}$ measurement, whereas no $\chi_{\rm eff}$ measurement was capable of
confidently determining a system to be anti-aligned with the orbital angular
momentum at current detector sensitivities. These results indicate that
measuring spin-precession through $\chi_{\rm p}$ is a more detectable signature
of a hierarchical mergers and dynamical formation than anti-aligned spins.
