Background: As the COVID-19 pandemic evolved, concerns grew about its impact on pregnant women. This study aimed to determine how SARS-CoV-2 affects pregnancy, birth, and newborns, in order to identify vulnerable individuals and provide proper care. Methods: This is a retrospective case-control study of 398 pregnant women who delivered at the Emergency Clinical County Hospital in Sibiu, Romania from 1 February 2020 to 31 March 2022. Patients were initially grouped and compared based on their RT-PCR SARS-CoV-2 test results into the COVID group (cases) (N = 199) and non-COVID group (control) (N = 199). The COVID cases were further divided and compared according to the pre-Delta (N = 105) and Delta/Omicron (N = 94) SARS-CoV-2 variants. COVID cases and control groups were compared to identify correlations between sociodemographic factors, pregnancy outcomes, and SARS-CoV-2 infection. The same comparisons were performed between pre-Delta and Delta/Omicron groups. Results: There were no significant differences concerning maternal residence, while educational level and employment proportion were higher among the positively tested patients. No significant differences were found for neonatal and pregnancy complications between COVID cases and control groups. Except for a lower mean gestational age, no significant differences were found between pre-Delta and Delta/Omicron periods. The maternal mortality in the infected group was 0.5% (1 case). Conclusions: Our study showed that SARS-CoV-2 infection at birth did not significantly affect maternal and neonatal outcomes, not even considering the SARS-CoV-2 strain.