When I wired my boat I ran the alternator output directly to the start battery. The start and house banks are connected by a battery combiner so that both banks are charged when the alternator pulls the start battery up above the combiner's threshold voltage. In other words, the two banks are connected WHEN the engine is running and separate when the engine is off. I also put in a switch to allow me to interconnect the two battery banks so all the batteries can be used for engine starting if needed. ALL electronics, etc are connected to the house bank so that the start bank isn't drawn down by anything except engine starting.
For redundant charging I have my cabin top solar panels wired to a dual output controller that charges both battery banks. It is split 90% house, 10% start. I do not have shore power or a generator. 200 watts of solar panels on the house top lets me leave my refrigeration on full time and keeps the batteries at 100%.
In your case, I would leave the radar connected to the house bank.