My parents moved to Codington County when I was three months old and aside from a seven year stint in "college", I've lived and hunted here my entire life. I've got the good fortune of having access to private land as well as an ever growing knowledge of the public land in the area. The first thing I will say is that while there are birds around, there are a lot of pieces of ground that are "all in one", meaning they have food, cattails, shelterbelts and, in some cases, nesting/brood rearing grass all in one spot. Those pheasants don't "need" public land, outside of the ones that don't have nesting. While that is a challenge, there is some "spill over" onto public land near those areas, especially in the early season, where a guy and his dog can put a couple birds in the vest.
If it were me and my wife gave me the green light to bring my dog and shotgun, I wouldn't hesitate for a second. I am blessed and have wonderful in-laws, but that doesn't mean that small doses aren't great for maintaining that feeling. As the other guys noted, you would have a little bit of time to scout in the morning (depending on schedule and time allotted for hunting) and can look around. Find a public spot surrounded by a lot of corn and, in some cases soybeans, and you'll have a good chance of catching birds coming back to roost in the last hour of the evening. I'll say it again, if you're limited on when you can hunt, make sure that it is in the hour or two leading up to sunset.