Eventually, yes. But probably I think the first step will be to continue to grow the pie before they change the size of the slices. The "grow the pie" strategy will first be via the B1G/SEC scheduling arrangement to create more TV-friendly matchups. Because no one cares about Indiana vs. Vandy, that scheduling alliance will focus on the big brands.
The 2nd step will be the B1G+SEC either combining, or more likely co-negotiating their next TV deal. I don't think they'll merge in the next 15 years because they want to control their own destinies, but I could see them getting together to double their negotiating power, and cutting a deal similar to what the NFL did recently where they spread rights across everyone including streaming services like Amazon for a few games.
The 3rd step will be tiering the revenue distributions. This will separate the Miss St., Vanderbilt, Indiana, and Purdue tier from the Texas, OU, Alabama, Ohio St. Michigan tier. They'll still be in the same conference but they'll be paid differently and justified on viewership.
The B1G and SEC eventually turn into a AFC/NFC arrangement, and that holds up through other realignment moves like FSU and North Carolina because those brands aren't big enough to trigger the nuclear option of blowing up everything and creating a mega league like the Rudy proposal. This is the most likely outcome over the next 15-20 years because it's the lowest risk option. Maybe 20+ years down the road of being the AFC/NFC do the B1G and SEC eventually formally unify, but not before.
What the sports media is missing in the reporting of the Rudy and other PE-backed proposals today is the risk component, they're only factoring in the increased revenue. Risk and control matters, a lot. Here is a list of why the Rudy proposal and those like it to create a unified mini-NFL won't happen:
It's directly against the interest of TV rights holders by getting them to pay more for the same thing. Therefore they will work hard against it and pull whatever levers they have, just like ESPN sunk the PAC-16 by offering Texas up $300MM for the LHN knowing it was a poison pill for PAC-16. We'll see more of that.
It's directly against the interest of the SEC and B1G administrators, who would be out of a job if a PE-backed structure gets put into place. No one at the SEC or B1G office is going to fight for this, in fact they'll work against it.
As a result, if you're the PE group, you have to bypass the conferences and go straight to the university presidents. This is a notoriously fickle, risk-averse, and SLOW decision making group who doesn't really know about the business of college football. If you're a lifelong academic university president, do you trust the AD you hired and the conference commissioner you've known for some time, or do you trust this new PE suit who is showing up promising big bucks if only you change everything? Past evidence suggests strongly they'll choose the former path.