Yes a small battery could be a option.
1000watt / 48V =20,83A 36V 27,77A or 24V 41,66A
With actual battery technic possible, 100x NCR18650PF(3.7V 2.9A) 10s10p give 37V and 29A 1,073kwh, so you would discharge under 1C.
But the question is, how much cycles/day you would get, and how long you would puffer till shutdown.
Con the inverter costs extra, and also the battery charger maybe balancer. There are few diy power walls

1 KW from a 4-battery series connect of car-type or standard lead-acid deep cycle batteries is a fairly low load - car batteries in particular are rated for "reserve capacity" in minutes at a 25 amp draw.
It would also be not bad for a 2-battery series setup at 24 amps, well within the rated capacity of the batteries though you might see a small reduction in the "rated" amp-hour capacity.
Not even close to the typical 500 VA UPS that runs from a single 12V 7AH gel cell (and DOES show a massive reduction in battery capacity due to the very heavy draw).