If it is a dense foam, usually black or dark grey, it will probably be fine. If in doubt, you could test it on something that would not matter if it dropped off.
Ideally, badge, car and tape need to be warm! Many number plates have dropped off after being applied cold. (Usually about 7-10 days) Tape and badge in house works, but car would need warming. Park it with the sun on it, then add heat from a hairdryer until car is almost too hot to touch. Difficult this time of year unless you can get it into a garage. Don't use a hot air gun, it takes the paint off.