Yes, you would need to setup a Post-processor for the GRBL (Arduino); In CopperCam, in the menu, click on Parameters / Data Output Format, and then click on the Format: combo-box, click on Post-processor "ISO standard" bottom of the list. A dialog box will open for you to write your own Post-processor. The g-code is not that far off... You have six decimal places, you only need three, the z-axes does not need to be printed on every line, and the lines with I### and J### are curve coordinate....
You probably need to check out GRBL (Arduino) for the Post-processor format...
GRBL (Arduino) may even run the ISO standard...