Sure, I imagine that in this day and age of hyper negotiated CBAs and rules about player events and what days they're allowed to work and the number of hours you can force them to practice much less interact with NHL fans that this idea likely wouldn't work. That being said I still love it.
Back in the day of the IHL and ECHL Roadrunners after early(-ish) Sunday games the teams would have an open skate on the arena ice. Sometimes they'd involve the players, (or just a few) and other times the entire team would be out there. Sure, it's a minor league type of thing to do to. In the minors no one really knows your players because they rotate around a lot. It's an easy grassroots way to connect with kids, their parents, and anyone that generally wants to hang out with the players. Would this type of thing work in say New York? Maybe. You'd have to limit the number of people, but how good would it look to finally see Sean Avery skating with some little kids?
The vast majority of players that I've ever spoken to or just seen video of are so incredibly friendly, with a few exceptions or course, that I think they'd have fun with it too. Sure, it's cumbersome to do and it could be a logistical nightmare, but I miss these small time, fan base connecting events. Sure the Coyotes have some different things each year. Coyotesfest, last year they did a carnival, but it's actually something to be able to skate on the NHL ice surface and seeing the arena from down there on skates. Plenty of fans have been on the floor of the arena, but taking some laps around, not so many. So borrow some skates from the Ice Den or Polar Ice and let's get the fans on skates.