NO. High rate of discharge lowers the capacity and also reduces the battery lifetime. It's complicated and varies between battery chemistries. You ned to find the discharge rate at which the battery was rated.
What was not addressed so far is that 6.8 amps at 220 V is "equivalent" to
125 A at 12 V. Iow, A = P / V.
So, you would need an even *bigger* battery than your already very very large 100 A-hr battery.
And, a pretty expensive inverter. Altho an inverter providing 6.8 A at 220 may not seem like a big deal, the ability to handle much larger in-rush currents upon start up *is* a big deal.
And these are paper calculations, as well. Everything gets worse off paper, such as the voltage drop of batteries with discharge, IR drop, etc.
Now, if this were a car A/C, you proly would need *far less* than a ton of A/C, AND you probably wouldn't need it to be on for a solid hour, so you could make do with a smaller (separate) battery. But still a battery-demanding proposition, which is why the battery should be separate from the rest of the system, lest you become stranded.
If for an apt/ house, you'd proly need a pile of batteries -- but then, you'd proly have the room for this.
Fortunately, the newer inverter technology for A/C (mini-splits or ductless) seems to be pretty power-miserly, altho it is still a motor, but a much less gluttonous motor.
EERs for minisplits can push 20+, so you get much more bang for your A/C buck -- but a lot of bucks: these high-end A/Cs (fujitsu, mitsubishi) are perty pricey.
Inverter mini-splits can have net *triple* the EER of an old clunker, in particular old sleeve (thru the wall) units, which have notoriously low EER's -- they claim 8, but proly pushing 6.
If you were actually considering trying this, I'd get the smallest units possible in multiples, and "stage" them, to be kind to the batteries. Inverter technology in newer A/Cs already has a kind of built-in staging, but I'd still go with multiples of the smallest units -- which I think might be 9,000 btu (3/4 ton), but poss. less.
Oh yeah, and *lots* of batteries. :)
Mae West (yer fav Congressman) to the Gangster (yer fav Lobbyist):
A 100 amp/hr battery isoften a 20 hour rating - i.e., 5 amps for 20 hours. That means that the battery can produce 60 watts (12volts x
5amps) for 20 hours. If an inverter is 80% efficient, the output would be 48 watts at 220 volts.
For 1500 watts, you need 1500/48 = 31.25 times as much power input.
31.25 * 60 watts = 1875 watts into the inverter. 1875 watts at 12 volts is 1875/12 = 156.25 amps. This current level requires big cables and very good connections - better to use a higher battery voltage to reduce the current. At 24 volts the current would be 78 amps; at 48 volts the current would be 39 amps (this current level is likely within the wiring abilities of most DIYers). Four 100 Amp/Hr batteries wired in series for 48 volts might power that AC for half an hour.
Serious battery power (as in solar and wind powered houses) uses multiple large (200 Amp/hr or bigger) batteries to store power. However, they are more likely to use DC powered devices than to waste power generating AC via an inverter. (A 6 volt 200 Amp/hr battery can be moved by two people, anything bigger usually requires a hoist or forklift. Four of these in series make a 24 volt 200Amp/hr battery bank.)
There are DC versions of almost every appliance - many designed to work on a 32 volt marine power system.
I worked with a guy who got fed up with the continuous price hikes and poor service from his local electric company (north Mississippi). He set up a couple of Winchargers in the back yard and a battery bank (surplus from the local telephone company) under the carport. As far as I know, he used it for years until he moved back to South Carolina to be near family. He was way ahead of the current green movement, as he started doing this in the mid to late 70's.