Yes, you can use the portable inverter while engine is not running. But don't do this for too long, because this will drain your car's main battery until it's completely dead, and you will need a jump which is a hassle. I would say not to use the inverter for more than 30 minutes at a time if the engine isn't running. If you want to use the inverter longer, then simply turn on the engine for maybe 10 minutes at a time just to get the juice running again to prevent a dead battery.
I'm no expert, but I *think* the maximum is something like 10 amps for a vehicle's 12 volt outlet. That means 10 amps total for all devices used. Again, I'm no expert. I would suggest you to call a local Chevy service dept and ask them the question of maximum amps your vehicle can output from the 12 volt outlet.
I have blown my vehicle's 12 volt outlet fuse a couple times. It's a hassle. It's more of a hassle for me to have the fuse replaced which is connected to the van's main battery because I must rely on a mechanic to figure out where the heck the fusebox is located. But if I blow out a 12 volt fuse connected to my auxillary battery, that's not so bad because I know how to replace the fuse connected to the aux battery, and I keep an extra supply of spare fuses.
That's also why I sometimes prefer to use my auxillary battery's inverter (instead of 12 volt) because the auxillary inverter has an automatic reset with no replacement fuse needed. That's why even though my Dometic fridge can run on either 12 volt power or 110 power, I prefer to use 110 power so I don't have to potentially replace a blown fuse. For the inverter, there is no fuse to replace, the unit would simply reset if too much total power is drawn from all devices.