I wrote about rapid onboarding a couple of months ago. Rather than seeing it as the organization's responsibility, I was looking at it from the perspective of the employee. As an employee, what can you do to shorten the length of time it takes you to be fully integrated within your team and to add value to the organization.
Based on my experience of the past few months, I'm tempted to express some caution with this approach and to articulate some hypotheses.
Unless the organization is equally in a hurry to get you on board and fully committed to helping you out, don't rush. Whether a rapid onboarding approach is appropriate (and successful) or not may depend on factors totally out of your control as a new employee. Such factors may include 1) the extent to which you have regular access to your supervisor/management for feedback and guidance; 2) the extent of disagreement / conflict around your position.
Becoming part of a team or organizational unit has a lot to do with establishing relationships. This can't be rushed too much and if there is disagreement or conflict around your position, it may take even more time. If the environment is less than ideal, it should still be possible to focus on learning the culture, the jargon, the processes, and staying away from actually "doing" anything (especially anything that might be perceived as stepping in other people's territories), at least until things settle and you've had a chance to see more clearly what is going on and you're better able to interpret subtle cues and signals.
I'm assuming this isn't such an issue when someone is hired with a clear mandate to lead a team. Then you probably can't afford to wait and see. If you're in charge, learn quickly and act like a leader. If there is confusion about who is in charge and roles and responsibilities, then being in a rush to do things and to add value is probably not where the emphasis should be.