most likely not.
The " int LEDpin = 13; " that your typed is turned into instructions that are stored in FLASH or ROM or what ever the instructions are stored in. The "13" is part of the instructions.
You can type "" int LEDpin = [pin_name]; " where some where you defined pin_name=13. Same results.
You could type " int LEDpin = ; [pin_name]" Where you defined pin-name is at RAM location 100. And RAM location 100 has been set to 13 (load 13 into RAM100) Now the instructions will be different but the final results will be the same. At this point you can change RAM 100 to be 14 and get the output on a different pin at any time.
You can define pin_name to a EEPROM location. The code will look in EEPROM (address) to find what pin to use. Most likely the EEPROM will be loaded with numbers at compile and these will not be changed often. If you make 1000 computers with the same code but you want 50 to work with pin 13 and the other 50 to work with pin 14 you only need to reprogram one EEPROM location to change which pin to use.
Another example of EEPROM. My TV forgets most things when the power is removed. But it remembers what channel I was watching, what volume, what brightness, etc. That is stored in EEPROM when I make changes. And retrieved when I turn on the TV. (start up on channel 10 is not stored in code but in EEPROM)
All things depend on what type of computer! Most often the ROM or FLASH contains code and some data that can not be changed like "pin=13". No computers can change their ROM and likely can not change the FLASH. RAM is temporary data. EEPROM is data that is remembered during loss of power. You can read RAM and EEPROM exactly the same. Writing EEPROM take a long time. (very slow)