  Diffuse radio recombination lines (RRLs) in the Galaxy are possible
foregrounds for redshifted 21~cm experiments. We use EDGES drift scans centered
at $-26.7^o$~declination to characterize diffuse RRLs across the southern sky.
We find RRLs averaged over the large antenna beam ($ 72^o \times 110^o $) reach
minimum amplitudes between right ascensions~2-6~h. In this region, the
C$\alpha$ absorption amplitude is $33\pm11$~mK (1$\sigma$) averaged over
50-87~MHz ($27\gtrsim z \gtrsim15$ for the 21~cm line) and increases strongly
as frequency decreases. C$\beta$ and H$\alpha$ lines are consistent with no
detection with amplitudes of $13\pm14$ and $12\pm10$~mK (1$\sigma$),
respectively. At 108-124.5~MHz ($z\approx11$) in the same region, we find no
evidence for carbon or hydrogen lines at the noise level of 3.4~mK (1$\sigma$).
Conservatively assuming observed lines come broadly from the diffuse
interstellar medium, as opposed to a few compact regions, these amplitudes
provide upper limits on the intrinsic diffuse lines. The observations support
expectations that Galactic RRLs can be neglected as significant foregrounds for
a large region of sky until redshifted 21~cm experiments, particularly those
targeting Cosmic Dawn, move beyond the detection phase. We fit models of the
spectral dependence of the lines averaged over the large beam of EDGES, which
may contain multiple line sources with possible line blending, and find that
including degrees of freedom for expected smooth, frequency-dependent
deviations from local thermodynamic equilibrium (LTE) is preferred over simple
LTE assumptions for C$\alpha$ and H$\alpha$ lines. For C$\alpha$ we estimate
departure coefficients $0.79<b_n\beta_n<4.5$ along the inner Galactic Plane and
$0<b_n\beta_n<2.3$ away from the inner Galactic Plane.
