I have not tried doing what you propose, but I am very sure they will swap directly. Many cars I see had those badges swapped.

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80 300SD (129k mi) 82 240D stick (193k mi)77 240D auto - stick to be (153k mi) 85 380SL (145k mi) 89 BMW 535i 82 Diesel Rabbit Pickup (374k mi) 91 Jetta IDI Diesel (155k mi) 81 VW Rabbit Convertible Diesel 70 Triumph Spitfire Mk III (63kmi)66 Triumph TR4a IRS (90k mi)67 Ford F-100 (??)