The league would blow up, because if you would read that article, the initial process to impeach Sterling, if you will, starts with a written charge from the league to Sterling, and Sterling has five days to respond. Something tells me he wouldn't be in a mood to grease the wheels on such a process. Once he responds or his window has expired, a meeting with the board of governors is scheduled, evidence is presented, and then the governors vote. So even if everything is expedited nicely, you're still looking at over a week of delays before a resolution. It's not like the rest of the world revolves around the NBA, so there may well be scheduling issues involved with moving the entire slate of games back a week or two. The draft may have to be rescheduled. This isn't minor stuff.
Sterling has no leg to stand on if the league does it right, but if they do it wrong (which they would be more likely to do in the panic of a player strike)? Then a real shitstorm could brew and Sterling could strike back with a lawsuit. Which is why this is best saved for the offseason, letting justice come naturally instead of trying to rush it.