Yes, your complete '71 bumper will fit if you have every part of the bracketry.
Here's some help on the front end:
& then you just need a couple of old front fenders (or the park light areas from a set of bad fenders).
Once you look up under a chrome car, you'll understand how to adapt the rails to attach a front bumper.
The rear requires the 2 small pieces from under a chrome car's taillights...they're available new from Moss.
You'll also have to build a bracket to bolt the rear bumper assembly to the holes where the rear rubber bumper attaches.
Then, you'll have to lower the entire car to achieve a chrome car's stance.