Yes, that is an operational block diagram of a typical solar system. You may wish to separate the (+) phase wire from the solar charge controller and converter to the farthest left battery so that current flow is better balanced but what you have there will work.
It may help to think of the solar system as just another battery charger.
BTW, you should have some circuit protection like fuses or circuit breakers inline with the output of the batteries and between the batteries and solar controller. FWIW, I also added a manual circuit breaker between the modules and solar controller. That allows for disconnection of solar power should I need to work on wiring or the batteries.
Edit: I missed it but I guess you have two fuses in your drawing. Attaboy!