  We present results from simulating slitless spectroscopic observations with
the Nancy Grace Roman Space Telescope's (Roman) Wide-Field Instrument (WFI)
P127 prism spanning 0.75 $\mu m$ to 1.8 $\mu m$. We quantify the efficiency of
recovered Type Ia supernovae (SNe Ia) redshifts, as a function of P127 prism
exposure time, to guide planning for future observing programs with the Roman
prism. Generating the two-dimensional dispersed images and extracting
one-dimensional spectra is done with the slitless spectroscopy package pyLINEAR
along with custom-written software. From the analysis of 1698 simulated SN Ia
P127 prism spectra, we show the efficiency of recovering SN redshifts to
$z\lesssim3.0$, highlighting the exceptional sensitivity of the Roman P127
prism. Redshift recovery is assessed by setting a requirement of $\sigma_z =
(\left|z - z_\mathrm{true} \right|)/(1+z) \leq 0.01$. We find that 3 hr
exposures are sufficient for meeting this requirement, for $\gtrsim 50\%$ of
the sample of mock SNe Ia at $z\approx2$ and within $\pm5$ days of rest-frame
maximum light in the optical. We also show that a 1 hr integration of Roman can
achieve the same precision in completeness to a depth of $24.4 \pm 0.06$ AB mag
(or $z\lesssim 1$). Implications for cosmological studies with Roman P127 prism
spectra of SNe Ia are also discussed.
