You can add invoicing roles to the agent.

Time marked with "Invoicing" is summed into «Invoiceable time» in the case.
 

 
When tick box for «Invoicing» is marked in work log, time is registered as «Invoiceable Time»:
 

 
Invoicing is defined on user level and in «Admin» tab we can choose which users to invoice and who will not be invoiced. If user is set to be invoiced, Invoicing tick box will be automatically activated for all   logs and emails   which will be registered in this case.