This year, the committee went strictly according to their own final regular-season rankings. The at-large bids in the non-playoff Big Six bowls were taken by the teams ranked 5 through 10, with the ACC's contract bid for the Orange going to the No. 12 team, GT, and the "Group of 5" slot going to No. 20 Boise State.
Suppose this year, ND had finished No. 11, right behind No. 10 Arizona. Would the committee have put ND in the Fiesta Bowl over Arizona? I think they could, but I very much doubt that they would.
Hence my caveats over how high ND would need to finish to be "guaranteed" a Big Six bid, especially in a year like 2016-2017 when non-contract bids will be at a minimum. If the 2016-2017 arrangement had been in place this season, the result would've been very similar to what we had this year -- the teams ranked 1-10, 12 and 20 would've made the Big Six. But at least 4 of those top 10 teams -- the Rose and Sugar opponents -- could've received those bids without finishing in the top 10, and the same is true of the Orange Bowl bid allotted to the SEC, Big Ten or ND.
If ND finishes in the top 10, its chances will be good in any season to make a Big Six bowl, but whether that bid will be guaranteed will depend on the season.