Introduction Acute Suicide Risk (ASR) is widely evaluated at Emergency Departments (ED). Little is known about follow-up of ASR after psychiatric ED evaluation, and if there are differences within No ASR (NASR) counterparts at baseline and afterwards. Method We developed a naturalistic, 3-month follow-up study of adult patients from a psychiatric ED in Mexico City. Depressive patients who asked voluntarily for an emergency consultation from July 1 to December 1, 2014, were included. We compared depression severity, suicidal ideation, adherence to treatment, and perceived social support scales both in ASR and NASR participants at baseline and follow-up interviews. Results Participants (n = 120) were divided into ASR or NASR groups (n = 60 each). The ASR group obtained more negative scores in all scales at baseline evaluation. After three months, 85% (n = 51) of ASR and 75% (n = 45) of NASR completed the second interview. 5.21% (n = 3) of participants showed new suicidal behavior. At follow-up, the ASR group showed a higher relative response in depression scales and treatment adherence (p = 0.036), and lower scores in suicidal ideation scales than NASR group (p = 0.012). Perceived support from family was significantly higher in the NASR group (p = 0.016). Discussion These relative higher responses in clinical scales suggest a paradoxical advantage of ASR over NASR patients, suggesting a hypothetical phenomenon similar to “The Tortoise and the Hare” effect. However, it is not applicable for all ASR patients. Results suggest suicidal patients experience stigma from their families. Further research and public health programs for ASR at ED should be implemented.