Microwave watt does it vary according to temp settings
To your title, the answer is maybe (or yes if you average over a long enough time).

To the body of your question - the answer is it probably won't work.  Here's why: 
The microwave is meant to put out 700W.   It's not 100% efficient so will consume more than that (also for the light and turntable motor).  

Most microwaves reduce their power by being fully on for a few seconds, off for a few seconds.  Some models have a type of inverter inside, and run at a lower continuous power but these tend to be higher-power models (mine, for example, is rated at 1000W).

Even then, your 600W inverter might be 600W peak or 600W continuous.  If it's rated to 600W continuous, it may be able to handle peaks of 700W+, but quite likely not for long.  It may also not be able to deliver its full rated power into a microwave - not all loads are created equal and the rating is probably for something simpler to drive such as a heater.