Depending on how much it overlaps, it could block or impede airflow in certain areas of the grill. The grills have airflow designed into them to provide what the manufacturer thinks is the best for that particular grill, which includes ambient probe placement.
I wrap mine on the Traeger and the Yoder, but I have always made sure there isn't any excess hanging over. If there is, just make sure it is tightly wrapped around the tray and not left hanging to block any air. On the Yoder, they specifically mention the use of foil and caution against it because if it hangs over, it could impede airflow. The drip tray on that grill leaves very little room along the front and back of the grill, so I could see how it may cause issues there. But the large roll Costco sells is the exact width of the drip plate, so it is just a matter of cutting to length and wrapping the two ends. I do the same on the Traeger. When I got the Traeger, they sent me the wrong drip trays. When they finally sent me the right ones, I was already used to using the foil, and never opened them.
But I always made sure nothing was left hanging over. It was always wrapped and pressed up tight against the back of the pan with as little as possible to ensure it wasn't hanging down underneath
If someone is having problems maintaining temps or reaching temps or possibly eratic fluctuations and is using foil wrap on the drip tray, it would be prudent to remove the foil and test the grill again to see if the foil may have been affecting air movement