If access to savings accounts helps the poor manage risk better, the answer may very well be "yes". A new working paper on Transactional sex as a response to risk in western Kenya reports that sex workers engage in better compensated but riskier sex acts following unexpected health shocks. From the abstract:
Formal and informal commercial sex work is a way of life for many poor women in developing countries. Though sex workers have long been identified as crucial in affecting the spread of HIV/AIDS, particularly in Sub-Saharan Africa, the nature of sex-for-money transactions remains poorly understood. Using a unique panel dataset constructed from 192 self-reported sex worker diaries which include detailed information on sexual behavior, labor supply, and health shocks, the authors find that sex workers adjust their supply of risky, better compensated sex to cope with unexpected health shocks, exposing themselves to increased risk of HIV infection. In particular, women are...19.1 percent more likely to have unprotected sex on days in which a household member falls ill... [these results] suggest that sex workers are unable to cope with risk through other formal or informal consumption smoothing mechanisms.
The authors of the paper also suggest that "sex workers may be better able to reduce their risky sexual behavior if their children and dependents had better access to health services or sub-sidized health inputs."