Gaia Data Release 3 has provided the astronomical community with the largest stellar spectroscopic survey to date (> 220 million sources). The low resolution (R~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 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 ${{\ \rm per\ cent}}$, 33 ${{\ \rm per\ cent}}$, and 56 ${{\ \rm per\ cent}}$ 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 α-elements. We find an absolute carbon abundance uncertainty of σA(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 α-element abundance measurements using BP/RP spectra means that efficiently obtaining these abundances will be challenging.