I guess we'll see but there is no historical evidence that the owners have the will to miss a full year of baseball. The 1994 strike cost MLB the entire 1994 postseason and the world series that year and lasted throughout the offseason, but in the end the owners caved and settled without the cap they had demanded. They lost about 33% of the 94 regular season and playoff revenues, and that was enough to force them to capitulate when the players made it clear they were willing to sit out the 1995 season. I personally don't think the owners are any better situated now than they were then. The primary difference is the value of their franchises relative to the expenses they'll incur regardless of whether they're paying players. They could tap those resources if they have to, but I don't think they will.
It's going to be ugly when it comes, but I don't think there's any chance a plurality of owners will be up for a year of lost revenue, let alone the damage that may do to the value of their franchises.