I have noticed that, whenever my MEGA2560 is plugged-in to the computer that I can unplug the 9V barrel connector power cable and it will stay on. That must mean that it is taking power from the USB connector. Does that mean that I should unplug my 9V Barrel Power cord from the board before I plug a USB cable into the computer?
No it does not mean you have to unplug the barrel jack.
It is clever enough to swap itself over to what it needs depending on what is plugged in.
Only caveat with most of the Arduino boards is to try stay under 10 volts on the barrel jack especially with REAL Arduinos.
Clones tend to be a little more tolerant.