The English translation of the datasheet has no specification of minimum and maximum voltage. There are some pages around that talk about the VIO specification (3.6 to 1.75V) as being the input voltage range, however that's only for the IO drivers.
So the question is, over what voltage range is this thing stable and how much current does it consume?
Test conditions were, an ESP-01 board with both LEDs removed and a 330uF cap directly across the board input power pins. Power was supplied by a Tek lab supply and current monitored with 5.5 digit bench DMM. A Lua script was run on power up that connected to the WiFi, connected to an MQTT broker, got the temp from a DS18B20 temp sensor, published the temp, then when into deep sleep for 10sec, & repeat.
Minimum Voltage: At the low end, the device did not reset correctly 100% of the time by about 2.2V, 2.3V seemed stable. Therefore 2.5V should be a pretty safe bet.
High Voltage: Noting that I'm taking the device beyond what is spec'ed as the maximum VIO. This is probably only doable at low temps, and only because it's a cheap device (don't care if I kill one.) I took the device up to 4.7V without any sign of problems, albeit slightly higher current consumption. Probably not safe to have it that high for extended periods... Still it's well above the 4.2V of a LiPo...
Current Consumption: The ESP-01 board with no leds in deep sleep mode consumes about 30uA @ 3.3V. This sounds about right, with the datasheet stating 10uA for the ESP8266, however there is also a flash device on this board fully powered on all the time.
At lower voltages there was no significant reduction in sleep current.
As the voltage increased above about 3.8V there is exponential increase in sleep current. It is likely some junctions are starting to become forward biased within either the ESP or flash. At 4.5V, the sleep current increases to ~2.5mA, or around 100x what it is below 3.8V. Given PN silicon junctions have a temperature dependent breakdown voltage, it's pretty likely that current consumption will increase with increased temperature.