Ok, I'm no expert but on your first question, I cant say how much it hurts the value of the car but obviously an original matching numbers car with original tags is always the most valuable.
On your second question, the answer is Yes. Many people for whatever may find cause to get a reproduction door tag. Google MARTI and you will find they sell vehicle manufacture reports for all mustangs built from 67'onwards. Also, they sell reproduction door tags.
The find step is to satisfy yourself the car is an original Mach 1. If so, your can purchase a MARTI report for the car (cost $70-100) and it will tell exactly all the manufacturing specs for the vehicle based on the VIN you will need to get from the chassis. The report will tell you the original color, transmission type, DSO, interior color, axle, etc for the vehicle. Armed with that information, you can order a reproduction door tag for your vehicle. I have seen several restored vehicles at shows where the owner has purchased a new door tag simply because the old one was lost, damaged or simply damaged over time.
.