That's 600w at 110v, or 60A at 12v. (Grossly - allow some slop for inverter losses.) This is roughly what my Sharp AC consumes when the compressor is running. Typically you would have to size your inverter to allow for a starting surge of up to 5x. I use a 2800w inverter, might be able to go smaller with soft/hard start.
That part is easy. The fun comes in battery life. Assume a reasonable evening, so the compressor cycle is 50%. That gets you 30A consumed per hour. If lead acid batteries, then Peukert is going to increase that a bit. Sooooo, with a 600Ah lead acid battery bank, held to a 50% DOD, I get 300Ah/30 or about ten hours. Maybe better if I use the energy save setting, which I don't, because of noise and temperature swings.
Bottom line, this is right on the border line for overnight use, especially in warmer, more humid climes.
Solutions?
-- Bigger, lithium iron battery bank.
-- True 12v compressor.
All of the efficient mini splits actually use a dc compressor that is infinitely variable, which is where some of the efficiency come from (variable compressor speeds). Apparently they generally run on higher DC voltages though, so some inversion or step up would still be required.
Your math looks spot on.
Ours pulls ~450 watts. 37 amps per hour (our batteries float at mid 13s) so probably slightly lower on amps. 50% duty cycle, rounded up for inverter and transformer losses, 20amps/hr. 400 amp lithiums at 80% discharge = 320 useable amps = 16 hours at 50% or 8 always on.
Other factors to consider is how long your solar array takes to fully charge your batteries the next day if you take them down to their respective full discharge/if you are also running AC during the day. Ideally the system would be sized to fully charge from full discharge while still allowing enough solar to use Ac during the day and maintain other vital camper functions. LeishaShannons rig has 1200 watts fixed high efficiency LG panels and 400 watts of lower efficiency panels and they still occasionally have to run the truck.
Short answer is it takes a very efficient AC, a ton of Solar, and you'll still probably have to occasionally run the truck in the hottest climes.
Our interior space is fairly small and very well insulated, so I'm hoping my duty cycle will be closer to 25%, but I don't have any real world numbers on it yet.