MCP73833 suitable for charging battery and system at the same time?
I don't believe you are supposed to use it in this manner.  Datasheets aren't necessarily the best place for application information.  Instead look for application notes and reference designs on the manufacturer's website.  These will give a good feel for the intended use.  

In this case, there is an example of a reference design that has a switch that allows the input voltage to disconnect the load from the battery while simultaneously driving the load itself.