Centaur on shore power to start battery while starting - ok?

I have a centaur 12/60 charging a 12v start battery.

The positive goes to the battery terminal while the negative joins the in-side of a shunt, joining with another negative in from the engine starter with the other side of the shunt obviously going to the battery. This should Iet me see the Centaur charge current through the shunt.

There is a 3000W starter motor on the diesel.

Can I leave the Centaur turned on when

a) I start the diesel, despite the huge but short current draw?

And b) while the alternator is charging the starter battery?

Can I leave the Centaur turned on when

yes this should be ok, the charger will go into constant current mode - however, if the battery voltage dips too low, and the charger can sense low battery voltage, it may either turn off temporarily or go into a precharge mode if it has these facilities.

charging with alternator should also be no problem, as the charger is voltage limited and will not produce current if the battery voltage is higher than the programed charge voltage.