Somehow the PO of my car did exacly what you describe. He pulled on the mast of the antenna until it separated from the base. Although the removable mast was great for dealing with the car cover I can think of 2 reasons why you wouldn't want to do this.
1) The mast isn't supposed to come off so when it was put back on for driving the radio got lots of static from the mast shaking, ,jiggling, and making intermittent contact with the base.
2) I eventually hit a really big bump and the mast fell off. I then had to remove the antenna anyway to put a new one on.
I say you find a better way to make the hole. It's not worth it in the long run. I say you remove the antenna from the fender temporarily and use the antennna hole to find the spot on the car cover.