Agreed. The converter will be at 13.6 and if your solar's float voltage is the same you can leave it on. If the solar's float voltage is higher than the converter's, then your batteries will go to that higher voltage and stay there all day.
When camping I keep the solar voltage high but it only stays that high for a short time after getting there in the afternoon till dark. If it would get that high in the morning and stay there all day, I would change that.
In my case I leave the controller settings as is (high) and turn off the solar (switch is on the array side--don't let the controller be on array but not battery) when on shore power. If I didn't have shore power but was not camping I would reduce the controller voltage to a float setting in the low to mid 13s.