You cannot engage the REx until the battery SOC is <=75%. This is to ensure that there is some 'space' to store the REx energy output. Once engaged, it tries to run at least long enough to warm up fully (about 10-minutes or so). After that, it will turn on/off and adjust RPM (and therefore output) based on how you are driving and the actual load on the car. If you manually turned it on, you can turn it off unless the SOC is at or lower than the automatic engagement value (you cannot adjust that). If there's no gasoline left, it will function essentially like the BEV does (minor possible exceptions). FWIW, the computer doesn't actually 'drain' the gas tank...there will be some unusable fuel left in it so that you don't damage the fuel pump, make it difficult to prime the lines, or overwhelm the filter.
2014 i3 BEV, 2021 X5 45e
(The i3 will be sold soon, <17K-miles, interested?)