We have a dodger on our 356. The windshields and side panels zip out and we've used the top alone many times as you describe, as a sort of small bimini for the companion way when it's nice to have shade. With a short connector piece, the dodger zips to the bimini, too, making an uninterrupted roof from in front of the hatch to the stern rail.
As to needing a dodger on the Great Lakes, there's not much you trully "need" on a pleasure boat, I guess, but the dodger sure has come in handy for cruising in the rain, keeping the cold breeze off the cockpit at anchor, and allowing us to anchor or berth with the hatch open during rain/cold. We added it to the boat later, and have used it and enjoyed it much more than I had even expected. If you're going to get the little hatch bimini, I'd recommend going ahead and getting the side and front panels, too, or at least having zippers, etc., added to the bimini so you could add the other pieces later.
Finally, remember that if you make the little hatch bimini too little, it will often be throwing its shade somewhere other than your hatch. Might as go full bore now, in other words, and get a bimini top that is as wide as it can comfortably be.
