Try This...

1. File > Document Set Up
2. Click each of the color boxes you see there in the Transparency section. There are 2.
3. The color picker will pop up when you click the color box
4. Set both boxes to the grey you want to use for the background.
5. Click OK
6. Now choose View > Show Transparency Grid from the menu.

This will show you a grey background on the artboard but the grey will not export.

Try This...

1. File > Document Set Up
2. Click each of the color boxes you see there in the Transparency section. There are 2.
3. The color picker will pop up when you click the color box
4. Set both boxes to the grey you want to use for the background.
5. Click OK
6. Now choose View > Show Transparency Grid from the menu.

This will show you a grey background on the artboard but the grey will not export.