Is it possible to copy my sketch FROM the Arduino back to the IDE?
Your sketch never made it to your Arduino, so no.
I was not clear. I have my sketch in my Arduino. I want to download the sketch from the Arduino back to the IDE.
No, there is no sketch in the Arduino.
Your sketch was written in C++.
The AVR microcontroller on the Arduino board does not understand C++, so your sketch was compiled into AVR machine code.
What you are asking is a little like asking for your eggs back, after they've been turned into an omelette.
(well, not quite as irreversible as that, but since you had to ask the question, I simplified it a bit)
You can get the compiled binary back as a hex file - you could in this way copy it to additional boards using the same processor. You cannot regenerate the code that you compiled to get that though- the information needed to do that isnt present on the board.