Shortages of human resources for treating HIV/AIDS (HRHA) are a fundamental barrier to reaching universal antiretroviral treatment (ART) coverage in developing countries. Previous studies suggest that recruiting HRHA to attain universal ART coverage poses an insurmountable challenge as ART significantly increases survival among HIV-infected individuals. While new evidence about ART's prevention benefits suggests fewer infections may mitigate the challenge, new policies such as treatment-as-prevention (TasP) will exacerbate it. We develop a mathematical model to analytically study the net effects of these countervailing factors. Using South Africa as a case study, we find that contrary to previous results, universal ART coverage is achievable even with current HRHA numbers. However, larger health gains are possible through a surge-capacity policy that aggressively recruits HRHA to reach universal ART coverage quickly. Without such a policy, TasP roll-out can increase health losses by crowding out sicker patients from treatment, unless a surge capacity exclusively for TasP is also created.