I heard that ESP 8266 can be use as UART directly from fresh power up.
This information is misleading. New ESP8266 comes with a firmware that we can communicate with ESP8266 and tell it what to do using UART communication, not ESP8266 can be used as UART link by itself. If you want to make ESP8266 act like a wireless medium to transfer data from laptop to servo controller, you will need a new customised firmware installed to ESP8266, which can be done by Arduino.
For your case, if you wish just to transfer data between laptop and servo controller wirelessly, and the range is not too far, bluetooth is enough to do so. In Bluetooth case, Arduino programming is not needed.
Laptop -> Laptop bluetooth -> Wireless -> mobile Bluetooth -> serial data feed to servo controller.
To setup both bluetooth modules to enable pairing and automatic connect once power up, software such as PuttY and USB-UART converter are only the tools you need.