Something like this does really depend on the embedded culture of the company and the people in it. It's really hard to force it to work no matter how great it could be.
I worked at a large scale company and we implemented a HackDay event from the bottom up, modeled after what Yahoo and Altassian did. We simply just did it, grassroots style.
While management buy in can make it be better, it's not as necessary as employee buy in. If people are motivated enough, they will find the time to make it happen. Whether that's formal 20% time, a slow Friday, 120% time or just lunchtime, it will really come down to attitude and motivation.
Luckily I was in an enormous company at the time so the likelihood of finding compatible people was a lot higher. But it still took a lot of will power and effort to get it going. I've since parted ways with the company, but currently they're running their 10th event, so it's managed to stick and continues to grow each year.
Sometimes, these sorts of things, you just have to throw caution to the wind and just do it. Reduce the hurdles, bend the rules and make it work for your group. If it means taking a few days instead of one, or just shortening it to an afternoon of idea brainstorming, there's lots of ways to get people engaged. The important part isn't so much what actually gets done on a HackDay or how, the fun part is to get things started. Once the ball gets rolling, that's when you start to see the interesting things happen, and that will end up lasting far longer than any HackDay can.
I've seen our HackDays produce everything from personal learning experiences to website redesigns to online tools to new prototypes that actually went on to become products in the company's inventory. Undoubtedly something of value, yet the concept itself was still run adhoc by a core group of employees that believed in the concept.
Anyway, I have a little more about my thoughts on HackDay here: http://goo.gl/xNofr
And I figured I may as well, so here's to actually running a HackDay: http://goo.gl/zV8Wz
I know, cheap plug.