You can use the Electron without the LiPo if you have a power supply that can supply 2A, and do so fast enough for the very short power bursts in the cellular modem. You may want to disable the charging LED as well. If you don’t have sufficient power, you probably won’t be able to connect to cellular or connect to the cloud. It will also vary depending on how far away the cell power is (farther away = more power required).
If you have the LiPo connected, you can get pretty close to powering down by using System.sleep with SLEEP_MODE_DEEP for 10-20 seconds.