One factor to consider (depending on your locality) is that "unlimited" time off doesn't allow you to accrue vacation days, that would be paid if you were e.g. laid off.
Yes, we all have a lot of meetings and emails. But I fail to see how a project management tool addresses any of that.
Worse still, I don't get how this project management tool is any different to the many other project management tools out there (and how it is any less of a time suck).
Plus the sweepstakes "Send Your Boss to Hell" seems... random? Many of us aren't free to to our jobs, but a manager isn't (necessarily) the problem - often it's organizational structure. In any case, I wouldn't want a direct report to find out I'd won something with this name.