The i3 always is running off of the electricity (there's no connection of the engine to the wheels), but when the REx is on, it is applying power only to the motor and any excess back into the batteries. But, the REx engine is quite small, so if you let the batteries get drawn down near empty, the only power you'll have is the electricity provided by the engine (somewhere between 34-38Hp, not much - enough to let you continue as long as you're not trying to climb a long grade, where you'll eventually slow down since there's not enough power to keep going at speed).
So, the goal is to keep the batteries up above say 10%, and stop and refill the gas tank. Ideally, you'd reprogram the engine so you can manually switch it on earlier, otherwise, it won't come on by itself until the battery gets to 6% or so. If you program it, you can turn it on anywhere below 75%, and if you keep fuel in the tank, you can just keep going that way. The engine isn't super efficient, maybe mid-30mpg range while on batteries, it's closer to 113 mpge. When the batteries get down low, the engine will speed up, making it less efficient. Prior to that, if you've enabled it after programming, the rpm will vary to match the load. The REx is designed to hold the power (if possible) at the point when you turn it on. IT gets reset when you shut the vehicle off, though, so if you stopped for fuel at 50% charge, that's the highest it would ever get until you recharged the batteries at home or on the road.
So, 200-mile trip is totally possible, but you have to understand how things work or you'll be in for a surprise.
2011 535i x-drive GT, 2014 i3 BEV
Soon (hopefully!) A 2021 X5 45e will replace the above