Using Android phone without battery Some Android phones have removable batteries, and others are non-removable. It is the battery capacity that makes the device alive for hours. Also, the device can be used while charging. 

For an Android device with removable battery, is it possible to use only in charging mode (wall charging with the device's charger/USB charging) after removing its battery? 

(For example, a laptop can be run by direct plugging, 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