Can i charge one starter battery with split relay, then run my DC DC off the battery being charged?

Hey all

So I have a cataman and currently have one 12/30 orion Dc/Dc charger running off the port engine starter battery.

If i connect the starboard battery to the port via a split charge relay would this produce enough that once the port is charged it would activate the DC/DC charger? (I appreicate its not very effecient)

Also if i only started the port would this then be trying to charge the starboard battery and the house? As being as there is no input/output i assume tge relay would just open as the voltage increases, therefor potebtially delaying the house from being delayed? Or would the alternator cover both?

Ive attached a bit of a crude diagram of how would wire, just whether would work

Thank you