My mother is a gov't employee who travels for work, and I asked her if she'd ever been asked for her gov't ID. She said she's only been asked once or twice for it.
I guess if you're brazen enough to try it, go for it, but be willing to accept the consequences if you're asked for ID. I wonder if they card more for AAA than for gov't ID? AAA isn't always much cheaper than the lowest available rate, but I've been asked for my AAA card before.