I believe they can't come any lower than 3rd overall if they place dead last.
2023 NHL Draft Lottery Odds | Tankathon
NHL approves changes to draft lottery
As it stands now, the 'hawks according to Tankathon have a 25.5% chance of bedding the 1OA pick, and they can fall to no lower than 3OA. It still means only a 1:4 shot at getting Bedard, however. They also can fail to tank out and come into a lower position.
From a tin-foil hat stance (where I'm not serious about the following), I think if there was some conspiracy for the lotto to award a generational talent to a club, what would favor the league the most? I think it would be taking a high value team who is near the bottom of the league (Chicago/Montreal, the others are in playoff contention), and giving them a generational talent. Plus, Montreal won the lottery last season.