Am I correct to assume that any comments ( // .... ) in my code are ignored when it is compiled and uploaded to the board, so they will not affect the amount of memory used by the software ?
You are.
That's right. Comments improve readability with no overhead like program size or execution time.
What does increase increase memory (FLASH, SRAM) usage is if you have Serial.begin(), wire.begin() but don't actually use serial port or I2C bus. Some people start their projects from someone else code and didn't do a good cleanup.