The moment Blizzard announced team-specific Overwatch skins as part of its effort to make the game more watchable, it was pretty much inevitable that they'd become available to the game's skin-starved general populace as well. You won't be unlocking them the normal way, though.
In a video released today, OWL commissioner Nate Nanzer explained that team skins will only be available via a new currency called League Tokens. Nanzer said that Blizzard decided to implement this system "to ensure that the correct amounts from your League-related purchases go towards the teams".
— Overwatch League (@overwatchleague) December 4, 2017
On the upside, you'll be able to use League Tokens to purchase specific skins, which does sound better than cracking open a loot box and scoring a skin of a team you despise for a character you've never touched in your life. On the downside, it's another fake currency in a game that already has one, a sure recipe for convolution.
Nanzer said that when the system launches early next year, every player who logs in will be granted enough tokens to purchase one skin. He did not say, however, whether players will be able to unlock more tokens through MLG-calibre plays of their own, or if they will only be able to buy them.