Yes. The plastic card does not list what your license privileges are. You are supposed to carry the yearly paper one. And with the cheap plastic they make the cards out of, you don’t want to carry it around anyway. I used to for years. When I paid for my second replacement, I learned my lesson.I showed the plastic to a GW once, he promptly told me that I had to show him the paper copy because that showed all my licenses and certifications.
I got mine in 1993, and I’ve bought 5 others in the past decade.