Jan/Feb seems wildly optimistic... Approval and manufacture (and which vaccine?) still needs to happen, and that takes time, and we're 40 days from January. Also, if what I'm reading is accurate, it's a 2 dose vaccine 1 month between doses (though I haven't been following that closely, and that might not be every candidate.)
I mean, that would be amazing, but I don't see how the timing works out.
Realistically, though, they don't need fans in the seats to start the season, just need the players/coaches etc vaccinated... And making sure that all visiting players/coaches etc are also vaccinated. Fans by mid-late summer depending on how things play out.