I think the chances of this happening before expansion are basically zero. MLB wants two prime markets available who will build them a publicly-funded new stadium. They won't be eager for the White Sox to take one of those cities off the board like the A's did with Las Vegas. I'm not sure how eager Nashville will be to fork over nearly $1B in taxpayer money for a baseball stadium either as they're spending a fortune on the new Titans stadium.
After expansion? Mayyyybe. It depends on how the dust settles after expansion and realignment. I'm still doubtful that Ishbia, who is based in Chicago, will want to move the team out of state. But at that point, MLB wouldn't care because they'll likely have imploded the AL and NL, putting the Sox and Cubs in the same division and "conference" and thus making the Sox presence in the Chicago market seem superfluous. Still a longshot, but at that point, I could see a series of events that maybe leads to their departure - perhaps the city blocks the team from building a privately-funded ballpark at the 78 because of neighborhood objections and some other city ends up getting spurned by MLB in expansion and is ready to make a generous stadium offer. Maybe. But we're a long way from that point.
Most likely, if their only option is to stay at the current stadium and they won't or can't turn the area into a thriving "stadium district", then I don't expect them to move the team, but expect another 30 years of stagnant market share and arguing that Sox fans aren't fair weather even though they will only show up to games if they're winning and making deep playoff runs for an extended number of years.