Has a team ever made the tournament as an at-large in back to back years without appearing in the top 25, in either poll, during that time?
I'm guessing yes. I'll try to find an example.
I would guess it has happened quite a bit, but I could be wrong. All a team would to do is finish 5-8th in the ACC, Big East, Big 10 or Big 12 two years in a row and odds are they weren't in the top 25.
teams from smaller conferences probably do it often too. Like Creighton or other successful mid-majors. I bet Butler or maybe Dayton too. Be pretty solid in a mid-major and you will probably not be ranked, but probably get into the NCAA