Understanding the specifications on the Champion 3100 you do have a 30 AMP RV plug in on the side so I will assume you are using that, and plugging your TT directly in without any adapters.
According to the specs the Champion, nominal output is 2800 watts with maximum 3100 watts. With that said, under normal circumstances it will run your TT AC unit. However, if you have been running on battery for a while, there are variables which you may not be aware of when you start your generator and plug your TT in. You may not have anything else turned on, however, your TT converter will sense the power, and automatically kick on to charge the TT battery. Also, your refrigerator sensor to kick on the propane lighting ability will sense and if your refrigerator is set to auto, it may trip off running on propane and switch over to run on electricity. Also, there is the sensor to ignite the water heater with draws power if it is turn on, or even some water heaters will run on electricity and battery. Then there is the gas/carbon monoxide detector which is always drawing. All these components draw very little, but they do add up.
When you plug into the generator, put your ear next to your fuse/circuit breaker box/converter and see if you can hear fans kicking on. This would indicate it is trying to charge the TT battery.
Finally, with all this said, your AC is going to draw a lot. If you are running your AC while on the generator it is going to kick on to high load.
It should not go into overload. If the generator goes into overload it will trip its own circuit.
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