My inverter definitely works with 120vac 60hz. Some grid tie inverters I've seen are auto sensing to work with both voltages and frequencies, not sure if mine is like that. I don't plan to try anything other than 120v 60hz though.
It is interesting to watch the mppt work on a battery, there are youtube videos of GTI tests with voltmeters and ammeters running. Like this (not mine and not large batteries either but interesting)
I know what you are getting at with the mppt and large battery question.
My thoughts are that the inverter isn't going to go outside of certain limits for input current and voltage, and output power. I tested mine with two 6v golf cart batteries in series (12v), and it puts out around 100w. This is what I was expecting, since it is on the low end of the input voltage requirements. I asked several sellers with different GTIs with similar spec, and they all claim to expect around 100w max with a 12v battery. When I tested with a small 24v set-up (18ah), I could see it work the current and voltage until it was putting out rated power, then it didn't rise above that power level. As battery voltage dropped, it asked for more current. I can't comment on 24v with large capacity batteries yet, but I'll soon try it.