I'll assume that the motherboard is not touching the tray (except at the standoffs) since it was mounted there by Dell. If it is, then it will short out and nothing will work.
You didn't say why you want to put something between the tray and the case. I'll make a couple of guesses, but if they are wrong please explain why you are doing this.
- If this is to hold the tray in place because you don't have the right hardware to mount it in the case, I'd look for a better way to mount it. Ditto if you are doing this to cushion the tray for transport.
- If this is to stop a vibration problem then I would place some small insulators (foam would be fine) at several places on the tray. Avoid any hot spots.
- If this is because you don't like the idea of empty space inside the case, then I wouldn't do it at all. Airflow around the motherboard is good. Blocking it with foam insulation will only increase the temperature in the case.
- If the foam is near anything that gets hot, then this is a bad idea. In the worst case it could cause a fire. It could also overheat something and cause it to fail.