Yes. If you kill the Grox on one save file, then the Grox will stay dead on the other save file. Save files are completely separate up until the Space Stage, when they're basically all connected. They're all hosted in the same Galaxy meaning that any changes to territory (for example... the Grox) or alliances will be logged across all save files.
The only way to actually befriend the Grox after you've defeated them (assuming that you've absolutely DESTROYED and massacred every single planet and system under the Grox's reign) is to do a full scale Galaxy reset. This wipes every save you have thus so far (But you CAN back them up!) and basically makes the game act as if the galaxy was brand new.
If you want to backup your saves on Windows, do C:/Users/(windows username here)/AppData/Roaming/Spore/SPORE (Spore is Steam, SPORE is Origin) and then navigate towards the GAMES folder. This is where Spore saves your games. Select everything in that folder and then either move it to a new folder or paste it into a new folder.
Your galaxy will have been wiped, but your saves are still safe!