It depends on what your definition of competing is. If you're talking about super bowl? I doubt it unless Sam Darnold has an MVP caliber season. But for the playoffs, yeah.
Only one team will come out of the East and North divisions. It's possible that all three wildcards come out of the West, but you've got to think that divisional play will cancel one of them out. So that leaves up fighting with New Orleans and Tampa Bay for the division/3rd wildcard.
The more I think about it, maybe this move to get CJ was a preventative move against out competition as well.
With Horn's injury we definitely needed to add more depth to the position. But also note that Tampa Bay was window shopping for cornerbacks as well, they actually spoke reached out to Sherman before the Panthers did.
So maybe this was a move to take a piece off the board before the Buccaneers who have a suspect DB backfield.