Yes people outside your organization can see your home page if you allow them to. On the My Organization tab, choose Edit Settings. There's an option under the Security tab to allow anonymous access to your organization.
As an alternative, some people embed content from arcgis online into their own company web pages. For example, embedding maps or galleries, or creating web mapping applications from their web maps and linking to these.
http://doc.arcgis.com/en/arcgis-online/share-maps/embed-maps-groups.htm
http://doc.arcgis.com/en/arcgis-online/create-maps/create-map-apps.htm
Thanks,
Mike