Yes, they suggest that the minimum is 200Ah, because if you are thinking about it, if you draw full load from the inverter @ 4000W and 48V you draw 83 amps from the battery bank (losses ignored) - how long would a smallish battery bank be able to sustain that?
The 5KVA Axpert can charge the batteries at 60A via solar and 60A via utility and combine the two to 120A - it is recommended to charge the batteries at C10, thus you can effectively add a 1200Ah battery bank and still charge it without a problem. You may even add a bigger bank, but you'll have to manage it and ensure that you can keep the bank charged or not partially charge it and use it on a regular basis - here I'm not referring to the odd rainy day, but rather to daily cycling.