They don't turn you away, but you don't get to leave with the rifle in your hand either. They ship all of them. But still, you can make a trip and inspect (they will even loan you gages) and pick the exact one you want, pay, do the paperwork and that's what will arrive at your door. I think I'm going to cry when they run out of rifles. CMP has been around so long it seems like a part of "Americana" now. Also their armorers know what they are doing. When you get one from them you can almost make book that it's gonna run, headspace is correct, etc. At a gunshow? Not so much...
Actually, I believe you can walk out with your rifle(s). But you'll pay the local sales tax, which is considerably higher than the cost to ship the rifle(s) to you.