I found an article that notes that "data on the immigrant population, as recorded in the CPS, NHIS, census, and vital statistics, do not distinguish between naturalized immigrants, permanent residents, nonimmigrants (e.g., temporary workers, students, and visitors), and illegal immigrants" (Siahpush, M., & Singh, G. K. (2002). Ethnic-immigrant differentials in health behaviors, morbidity, and cause-specific mortality in the United States: an analysis of two national data bases. Human Biology, 74(1), 83-109). In other words, given the nature of the population, it won't be possible to get comprehensive statistics.

However, it might be possible to get a sense of trends for specific populations of undocumented immigrants. For example, this document mentions the prevalence of diabetes amongst Latinos:

Wallace, S. P., & Castaneda, X. (2008). Migration and health: Latinos in the United States. UCLA Center for Health Policy Research. http://www.healthpolicy.ucla.edu/pubs/files/Migration_Health_RT_English.pdf [PDF]

This article mentions higher rates of diabetes among migrants more generally, but does not distinguish between documented and undocumented people:

Argeseanu Cunningham, S., Ruben, J. D., & Venkat Narayan, K. M. (2008). Health of foreign-born people in the United States: a review. Health & place, 14(4), 623-635.

Is there a particular group of immigrants that you're interested in? Or perhaps issues associated with undocumented people and health more generally?