Most espresso machines are around 1000 to 1500 watts right? That's about 150 amps from the battery. A 150 Ah battery is NOT going to give you 150 amps for an hour. You might realistically get about 15 minutes from it. Most batteries are rated at the 20 hour rating, some at the 100 hour if the battery is a POS they are trying to make sound good. Reserve capacity does not really come into play much in this instance either for those who don't know any better.
Modified sine wave could be a problem. The heating element could care less, the motor not, might not want to run well on it. Some inverters as the input voltage starts to go low, the output waveform can get goofy which further aggravates the motor running properly for the pump issue.
Give it a shot if it runs, great, if not then take the inverter back and get your money back. Do yourself a favor though and use at least 3/0 wire for the main power cables to it. Yes yes I know 1/0 should work but for those kinds of currents for a few minutes at a time, you will cook your 1/0 after a while and the voltage drop won't be pretty either.
Might do better with a propane heater for the water.
Good luck.
Aaron