For conferences with a GOR (i.e. ACC), I believe the answer is "no." At least I don't think any school would willingly leave a conference to join a new conference unless the school can take its media rights with them to the new conference.

For conferences without a GOR, you may see some movement. However, I believe it will be primarily among the mid-majors because they may be at the most risk. In 1998, NE Illinois became the first NCAA DI member in recent years (maybe ever) to eliminate its athletic department. I do think you may see other smaller DI schools do the same thing or make the decision to switch to either DII or DIII levels in an effort to try and save money.