Apparently it does. I say this because they
STOPPED pushing them at the counter. I doubt this was a result of just me, though they heard it a lot from me as I'm a business customer and spend a lot of cash per year there. It's a bunch of people like me that get things changed. Perhaps they just decided to stop pushing it? We'll never know. I do know they haven't discontinued their magazine sales as they still have them listed at the counter and you can sign up through the credit card reader/signer device at the register.
A bit off topic, but similar. We have lax gun laws here in AZ. A law was passed that allowed you to carry a firearm in a restaurant that served alcohol UNLESS a sign was posted at the front entrance and by the liquor license. I frequently go into a Red Robin by my office and sit at the bar with my business partner for lunch. After going there for a few months at least once or twice a week they put up the sign stating no firearms. The sign was right there across from me, mocking me as I sat and ate lunch.

I told the manager that although I do not carry a firearm in public, I believe it's our right to be able to if we chose so.... particularly concealed where it's not going to make anyone nervous. I didn't go there for a few weeks. The next time I went back the sign was gone.
The same thing happened at the Denny's by my house. I take my kids there every couple of weeks and they started posting the sign there (even though they didn't even serve alcohol). I told the manager the same thing and I started going to another Denny's further from the house. Well a couple of months went by and I went there a couple weeks back because I didn't have time to go to the further one and sure enough, they too took the sign down.
Could all of this be a coincidence? There's a good chance. But it sure can't hurt. BTW, in my original post I mentioned making a "scene". That was probably a bit carried away... but it was a firm remark pointing out that I do have options when it comes to where I spend $$$. These business owners have every right to run their business within the boundaries of the law. As such, they have every right to post "no guns" signs... Just like them though I and others like me have the right to take our business elsewhere.