I have 4 BLDC motors, and 4 ESCs, one for each motor. But I have one LiPo battery from which I want to power one Arduino Mega and all the 4 ESCs. Can I remove the connectors from the ESCs and put them on a breadboard in a single column/row so that they are connected together, and then connect the + and - of the battery (after removing its connector as well) to the respective breadboard column/row, so that they are essentially connected together to power all the ESCs? Also, I would want to use a jumper from the Arduino Vin and GND pins to the same column/row on the breadboard. Will this method of powering all the 4 ESCs and the Arduino from a single LiPo work?
Powering all the ESCs from a single LIPO is not an issue.
Using a breadboard to distribute this power is highly unlikely to work, breadboard connectors are usually only good to a few hundred mA, 1A is you want to push your luck. Most ESCs and BLDC motors are in the 5A to 50A range (each, your power bus has to handle 4 times this current).
Also, ESCs tend to inject a lot of noise into the power bus. If you connect the arduino to the ESC power bus, you will likely get random resets and really poor noise performance on the ADCs. Keep in mind that some ESCs actively brake the motors using regenerative braking, which puts the kinetic energy of the motor back into the power bus. This can increase the voltage on the power bus to more than the nominal battery voltage and can have large voltage spikes on it causing a failure on the Arduino.
If you are prototyping, use a separate power supply/battery for the arduino and connect all the grounds together instead of using a single supply. If you are building a rover/uav/whatever and don't want a second battery, use a high quality BEC (or the BEC output from a high quality ESC) and remember that the 5V output on a BEC/ESC can be significantly higher than 5V in reality).
ESC = Electronic Speed Controlled BEC = Battery eliminator circuit (I think, basically a 5V-ish regulator) BLDC = Brushless DC motor (three phase in this case)