The odds against it are pretty long, particularly when the conference is producing elite teams that dominate non-conference play. The best chance would actually be highly tied to self-cannibalization scenarios.

The SEC has posted winning percentages of .857,.855, .793, and .828 in non-conference play the past 4 years; even giving the SEC a major bump over the best non-conference performance n history, to the .892ish mark shows why it is so hard to get 7 teams into a bowl.

The West will play 28 Non-conference games; if it goes 25-3, there will still need to be 17 conference wins distributed among the teams reasonably equitably to reach the mark. 17 doesn't seem so bad, until you delve into the zero sum nature of in-division conference play; 6 of the 8 SEC games each team has, would be either/or propositions; if one team is excellent, or two or three teams pretty good, it starts to skew fast--

SEC Conference play scenario:
Alabama goes 8-0
LSU goes 7-1 (loss to Alabama)
TAMU goes 6-2 (losses to Alabama and LSU)--

It means that Auburn, Arkansas, Ole Miss, and MSU are essentially reduced to 5 game slates, to pick up between 2 and 3 wins, depending on how the 3 non-conference losses within the division are allocated.

It seems simple, until you realize that of the remaining games, each will have head to head battles with another. 12 of those 20 games are essentially locked up among the 4. The most equitable pattern of getting to 6 wins for each team would be 2-1, 2-1, 1-2, and 1-2 splits among each other.

That'd logically lead two teams, at minimum, fighting to split their games against SEC East opponents, to pick up a 6th win-- more likely, 3 teams, as the aggregation of non-conference losses is more likely to happen at the bottom of the division than at the top of it.

Could it happen? It isn't outside the realm of possibility-- but it requires a historically unprecedented non-conference performance, paired with a completely muddled middle, and the domination of cross divisional play.

The more mathematically plausible scenario would be for a division to stack up with 1 team that goes 5-3, 5 teams that go 4-4 in conference, and one team that goes 3-5 -- then the burdens on non-conference performance would be immensely lighter, and the FCS/small FBS bowl division scheduling practices would make 7 teams to a bowl from one division decidedly more likely.