I can tell you from personal experience that as long as the law isn't abused by cyclist-hating lawmakers, it shouldn't impact roads you'd normally ride on. We have a major road in Memphis that runs through a large city park and has a section that's closed to bikes. It's busy enough and traffic moves fast enough that you'd really have no business riding a bike on it, but the fact that it goes through a large park and that it's a main artery to get into the east side of the city would be enough to draw some people try if it didn't have a sign saying that you're not allowed to ride a bike there.

Key phrase here being "as long as it's not abused"