Steem is much larger than Steemit, and that's why I try as much as I can to advise people to say Steem whenever they can, unless they really mean Steemit (which they rarely do).

The quicker onboarding will not come from Steemit, unless they give up the verification phase, which I doubt they will!

It will come from various other DApps which have been waiting for the opportunity. That's where the new flood of users will come from. And the DApps themselves, or their users will be the ones doing the promotion, but they won't promote steemit.com, they will promote the DApp, like DTube, DLive, Busy.org, SteemMonsters, Actifit etc.

I believe DApps which will have the process set up to sign up people using discounted accounts will let their users know, so that they can help in the promotion efforts to make that DApp known outside the Steem ecosystem and sign up more people.