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).
Yeah, a 48V pack comprised of 4 automotive SLI batteries in series is a reasonable solution, especially if only a few minutes of operation per day on average is required (that Peukert effect is a real bitch, and shows up even at 0.25C draw). Again, this is just for providing a bit of tolerance to the occasional passing cloud or, perhaps, thunderstorm; not to continue mining all night long.