Recharging flooded lead acid batteries is about 80% efficient. AGM batteries are about 90% efficient, but if overcharged, you cannot add water. ( to get 100 watts out, you need to charge with 120 watts - 80%) Holds true for any voltage.
If you have a DC source (generator) and it is running, it's power would be directly feeding the grid-tie inverter. The batteries may be "on-line", but in an idle state, or preferably, in "float charge".
for 4,000 watts (33.3A@ 120V), I would suggest as high as possible DC voltage as you can locate inverter/charger for.
96V : 41.6A
72V : 55.5A
60V : 66.6A
48V : 83.3A
because of copper losses in the wires.
30A household circuits require 10 ga wire (USA) more ampreage requires even thicker wire, both for safety and low resistance losses.
Of course, you will need proper DC rated fuses and circuit breakers, conventional AC ones will not work for DC, as the DC arc does not self exinguish.
If you are looking for something solar, to feed the grid, and reduce your electric bill, Grid tie can't be beat, as modern high voltage inverters [ 300 - 600VDC ] run about 96% efficient. I will use a generator for the rare blackouts. Eventually, as I move out of the city, I will have a grid-tie system again, and because of likelyhood of extended blackouts, a generator & modest battery bank.
View my current solar output
http://www.mike-burgess.org/images/GT_Screen_Save.png Updates every 10 min. Los Angeles daylight hours only.