The most popular 600 watt pure sine wave inverter for sale on Amazon.com is the Power Bright APS600-12. With no load it draws less than .85 amps and it has an efficiency rating of 90%. 600 amps is not enough to handle most coffee makers. My coffee maker, for example, needs 1500 watts. But as far as its draw on your batteries, I think it is an exaggeration to say it would drain your battery in very short time.
With NO load and running continuously it would need roughly 10.2 watts (.85 amps x 12 volts) or 244.8 watt hours (10.2 watts x 24 hours) and 20.40 amp hours (244.8 / 12 volts). Of course, if you turned your inverter on only when you needed it, or shut it off before bed, you would use MUCH less electricity stored in your batteries.
Now throw in why you need an inverter:
You said lights. Well, I thought lights in a RV are DC, which means you don't need an inverter for that.
You also said TV. The Jensen 28" JE2814 LED Television in my new RV needs 35 watts and 120 volts AC. So that's 0.291666667 amps (35 watts / 120 volts). However, that TV now needs the inverter. The 600 watt Power Bright APS600-12 (for example) has an efficiency rating of 90%. So the inverter will consume 3.89 watts (35 watts x 90%) or .32 amp hours per hour of usage, or 0.611666667 amps/hour COMBINED (TV + inverter). In other words, if you run just your TV AND 600 watt inverter you will be get 163 hours of TV from 100 amp hours of battery storage at 80 degrees F (BUT REMEMBER, to preserve the life of your battery you should not use more than 40 or 50% of your battery's capacity).
However, there are other items that will consume battery power regardless of your inverter: lights, CO/LP detector, refrigerator, etc.
So, that's how I understand the math. If I am wrong then I'm sure someone will correct me. And I hope they do, because this is how I calculate my own usage.