Yes. Lots of people carry different things. I don't carry this type of card, but what I do carry is a printed copy of state and local law and if flying on private property I try to obtain written permission and have that printed out as well. While I have never been approached by law enforcement I have been approached by security on a property I was filming. As he approached I reached into my back pocket for the email approving my flight, handed it to him, barely looking up. He read it, handed it back and said "have a nice day".
I tend to be very careful where and when I fly and so far anyone who has been close enough to speak to me has had nothing but positive remarks.