The homeless are a "composite" of individuals with a variety of issues which contributed to their condition....and, yes, a significant number do deal with substance abuse. "Substance Abuse and Homelessness – National - National Coalition ... www.nationalhomeless.org/factsheets...
National Coalition for the Homeless  "Although obtaining an accurate, recent count is difficult, the Substance Abuse and Mental Health Services Administration (2003) estimates, 38% of homeless people were dependent on alcohol and 26% abused other drugs." and "According to the Substance Abuse and Mental Health Services Administration, 20 to 25% of the homeless population in the United States suffers from some form of severe mental illness. In comparison, only 6% of Americans are severely mentally ill (National Institute of Mental Health, 2009)."  Of course these groups are not mutually exclusive, but both represent a significant part of the homeless population.   BTW: This has nothing to "off the hook" (cont.)