Android - Using Android phone without battery

AFAIK, no.

The fundamental reason is usage and the design that evolved based on it- mobile phone, as the name suggests, is meant to be used whenever and wherever, with periodic charging, unlike laptops, which are designed to work with/without being plugged into power.

It seems technically possible to work without a battery if you build an electric circuit that simulates a battery in all respects (including the battery health pin which is usually the third pin on battery) as you can see here. Whether such a circuit will work across OS versions and devices is not certain.

Android considers battery to be an integral part of the system rather than an accessory and OS evolves in safety, the longevity of the battery, user-friendly features, that support this - witness Battery Saver, automatic shutdown at low battery percentage as examples. If the electronics (SMBus) detects that it is not an actual battery source, this circuit may fail

Views expressed in comments are valid pointers, in addition to mine

My Infinix Hot 4 battery exploded and was left without one at home. I did this by drawing a circuit with a pencil on the motherboard from the GND pin to -ve pin. This tricked the phone that it has a battery on and it boots normally without one.