OK. Let's think about this rationally.
What we do know:
1) SOM mentioned they will get back to us on 3/27.
2) SOM started sending out invites on 1/20 (This is 1 working day after the video submission deadline of 1/15. Only 1/16 is a work day... I believe Yale and other NE Schools celebrate MLK).
3) SOM sends out invites in little spurts.
From 1), and assuming that they need 2 weeks to mull over interviews (reasonable assumption - many schools only mull for one week), we can approximate the last interview date to be 3/13.
From 2) and 3), clearly, they interview in batches (likely random). It is highly unlikely they would have went through the entire stack of applications within one working day and start sending out invites.
Typically, it is reasonable to give 2-3 weeks notice before scheduling interviews, as seen from the previous invites. Someone was only given 10 days notice yesterday or 2 days ago.
Lastly, from previous years/rounds, SOM sends out an email telling us that "interview invites are almost all sent out" or something to take extent. I'll take that email as a "ding without interview".
So, calm down... There is at least one to two weeks before all invites are sent, and even then, SOM will send "ding without interview notices" via email.