Yes, you can setup the live support mode for the chat and a social platform integration of your choice for example Easysocial, Jomsocial etc, however you can't work using the 'Filter by frienship' flag.
This can't be done and this won't work, because these 2 working modes can't live together. The live support mode is meant to be used with guests and sites that need to offer live support, where for example a super user is able to have guest users or common registered users in the users list, but common users are not able to chat each other but only with the super user in the role of the agent.
The filter by friendship flag is aimed to be used for chat usage on social community sites where users want to have in the chat users list only people confirmed as a friend. When you filter the users list query using the friendship filter for Easysocial, Jomsocial, etc the results of course will include only friends and nothing more.
The only working mode to use it as a live support tool and a community chat could be enabling the live support mode but not having it active for the public chat and chatrooms section. In such way the private chat can be used as the live support part and the public chat with chatrooms will continue to be accessible to everyone.