I think you know the answer to your question. If your property receives federal funding, you must declare all your advertising sources. You must make it known how and what avenues you use to inform the public of your housing services. As a single property, you cannot devote paid labor services to only one entity and not at least give the impression that you are partial to that particular organization. For example, if you only market to homeless veteran at a Catholic-run shelter, it could be questioned as to being a FH violation. And you definitely should not be volunteering there on company time. If there is an injury, it would then become a workman's comp issue and this may be hard for the property management company.
This is why companies often have a non-profit off-shoot that handles donations, etc. with a Board of Directors overseeing projects and money distributions, etc. What you could do, if you feel strongly, is 1. volunteer on your own time at your own expense and/or 2. contact the social service agencies in the area and see how you might coordinate efforts for your Apartment Association and them.
Obviously, you can market to the agency, to homeless people on the street, to veterans groups (VFWs) other homeless shelters in the area, etc. But for the sake of not seemingly favoring this one group or organization, I would just market to all avenues. Informing the local housing authority, as Nate suggested, is also a great idea.
So - spread the information, target this special group,too, as well as all other avenues, and don't look back! It is such a slippery slope to pin all your marketing to only one place, group, or area.