If you charge your battery fully after doing any testing like this it will most likely survive.
Your amp-meter will be accurate enough for your needs after learning to use it. While the meter can be less accurate for low amp readings, the low amp items are not what uses up the batteries.
Using the clamp-meter on your house-battery(s) to note detector usage, turning on a light or two (your normal evening light usage), running the refrigerator on propane, running an exhaust-fan, etc. Noting these different items as they increase the amp reading will give you a good idea of how many amps would be used if these items were each used for a single hour. The amp reading does get more accurate as the current read increases.
Checking your battery voltage at the beginning of camping (to insure fully charged) and then again after 24 hours (let battery rest with only detectors for about 1/2 hour), will allow you to see your current battery voltage (at the battery-terminals) and calculate the battery % charge versus the battery charge chart.
You can see how well your estimated usage compares to reality. Checking the extra amps drawn when using the inverter can be very helpful since these items are likely the real battery killers (high amp usage). They get added to the normal "house" usage).
The amp-meter can give you a very early warning if you check the extra amps being used to run your furnace in cold weather. That amp reading times the hours the furnace may be needed (plus the other usage) when checked against 50% of your total battery-bank can save you from a dead battery before morning.
In order to get by dry-camping you need to know when to cut back on unneeded items early in the camping period. Approaching cold weather may require skipping use of the television and other items.
By the way it's an electric motor running a compressor that requires a much higher current start-up. A motor by itself will start and run but if the required voltage drops (brown-out conditions) the motor will slow and you will see the dreaded "blue smoke" and a belly up motor.