Is there a standard report available that uses the 'chat_agent_sessions' table and sums the entire logged in time into one row?
November 2011 and newer releases - Analytics
The Chat Agent Status Summary report (ID 3027) has the logged in time compiled into one row. The Total Login Time column shows the total time all/each agents in the group were logged in for sessions that started during the selected date range.
You might also be able to create a custom report using the 'chats' table. The 'chats' table has the agent client ID and agent acct_id for the person who completed the chat. So you could use that, join it to the 'chat_agent_sessions' table and have a count of how many chats each person completed each hour. If a person transfers most chats and does not complete them, these numbers will look very low.
The 'chat_agent_stats' table also has a field called 'chats_completed'. Using this table would be much easier than using the 'chats' table, but data is purged from the table regularly. You would only have hourly stats for 30 days before it is thrown out. Between 30 and 180 days, you could get daily information very similar to the 'Chat and Cobrowse Activity' (ID 3046) standard report.
More information on database fields can be found in the data dictionary. Refer to Answer ID 2611: Accessing the data dictionary.
For information on other Chat-related reports, refer to Useful Chat Auditing Reports.