Generally speaking, it is beneficial for any business to support the local community through volunteering, lending support to community improvement initiatives, and being involved in any way that is beneficial to the local residents. This does include funeral homes.
I’m not sure exactly what you mean by a community outreach program, but a funeral home should strive to have a good reputation outside its doors – one where it is known by the people to be trustworthy. Most people have no interaction with a funeral home until there is a need and that can add to the discomfort of people needing their services or choosing another provider because they were not familiar with this funeral home.
To overcome this, many funeral homes choose to help enrich their towns in a variety of ways. Hosting a holiday remembrance service that is advertised and open to the public, sponsoring a food drive for the needy, volunteering at a soup kitchen, volunteering or sponsoring events at local schools. Any activity that gets the funeral home’s name out in a caring and helpful way will go a long ways in building goodwill and ensuring that the funeral home will be a trusted funeral provider when the need arises.