I thought the plastic card was the license and the paper part you get every year was tags? Like you would only need the card if you are fishing and not keeping an over sized red fish or hunting quail, hogs, squirrels.
You really should have the paper on you as well. The past three or four times I have been checked by GWs I normally give them the gold card and it's 'Thank you sir, have a nice day sir'.
I asked a friend of mine who is a retired GW this very question several years ago. His take on it is that it would depend on what GW you were dealing with. The majority that he knew would be perfectly fine with the lifetime card as long as it was not a tag issue, but probably not all GW's. There is apparently a little room for interpretation in the law.
My take on it is that the card is proof that I have a hunting license so it should suffice, but I make sure I get the paper one printed and have it on me whenever I'm hunting or fishing as a safety net.