That estimate of 3:1 undiagnosed to diagnosed may be low right now. It's certainly low for earlier periods of the year.

There's going to be a bit of a race between infection spread and vaccine rollout until they are both working together to reduce potential new cases. The vaccine will end up getting all of the credit, but the natural spread will have done most of the work.

It would be really nice if vaccine prioritization would put previous positive cases at the back of the line, but I haven't heard anything about that. Of course, even at that, we're going to be vaccinating a heck of a lot of people who probably don't need it because they have already had un-diagnosed cases (as "case" being defined as would have tested positive if they had tested at the right time).