  Gaia Data Release 3 has provided the astronomical community with the largest
stellar spectroscopic survey to date ($>$ 220 million sources). The low
resolution (R$\sim$50) blue photometer (BP) and red photometer (RP) spectra
will allow for the estimation of stellar atmospheric parameters such as
effective temperature, surface gravity and metallicity. We create mock Gaia
BP/RP spectra and use Fisher information matrices to probe the resolution limit
of stellar parameter measurements using BP/RP spectra. The best-case scenario
uncertainties that this analysis provides are then used to produce a
mock-observed stellar population in order to evaluate the false positive rate
(FPR) of identifying extremely metal-poor (EMP) stars. We conclude that the
community will be able to confidently identify metal-poor stars at magnitudes
brighter than $G = 16$ using BP/RP spectra. At fainter magnitudes true
detections will start to be overwhelmed by false positives. When adopting the
commonly-used $G < 14$ limit for metal-poor star searches, we find a FPR for
the low-metallicity regimes [Fe/H] $<$ -2, -2.5 and -3 of just 14$\%$, 33$\%$
and 56$\%$ respectively, offering the potential for significant improvements on
previous targeting campaigns. Additionally, we explore the chemical sensitivity
obtainable directly from BP/RP spectra for Carbon and $\alpha$-elements. We
find an absolute Carbon abundance uncertainty of $\sigma_{A(C)} < 1$ dex for
Carbon-enriched metal-poor (CEMP) stars, indicating the potential to identify a
CEMP stellar population for follow-up confirmation with higher resolution
spectroscopy. Finally, we find that large uncertainties in $\alpha$-element
abundance measurements using BP/RP spectra means that efficiently obtaining
these abundances will be challenging.
