Yes, a homeless person can apply for housing assistance.
Many waiting lists also have preferences for homeless applicants, which would give them priority placement on a waiting list. However, offices have leeway in defining this preference, and the specific definition tends to vary greatly by each housing office. Some offices may require applicants to be currently living in a shelter, some do not consider persons who are living with friends or family homeless, and others have much lighter requirements. Because of this flexibility, contact the office you apply through to confirm the definition of the Homeless preference.
You can use the search bar on the top of this page to search for housing authority and apartment community contact information.