I have never left it off so I don't know what it would do, but I would imagine it wouldn't do much of anything unless it was over filled. I could see problems with leaving in the old O-Ring (not really an O-Ring) or using the wrong filter (for the shallower pan) causing problems. I know that a co workers car was pretty bad off when the service place left the old seal in place and the filter sucked air around where the filter should seal.
97 Mark VIII LSC/Silver/Gray leather
97 Cougar 4.6 Sport/White Opalescent Tricoat Metallic /Gray leather down but not out?
89 Cougar LS 3.8/Oxford White/Gray velour/HG need replaced AGAIN
00 Grand Marquis LS/Vibrant White/Gray velour
63 Falcon 302/black and rust/shed isn't moving
82 F-150/Oxford White/dumb VV carb doesn't pass emissions