Interfacing 4 ESCs and an Arduino with a single LiPo battery
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)