I imagine it’s more that they’ll be a Klingon captain adversary. A Federation captain doesn’t fit in with Worf being the first Klingon in Starfleet thing.
Maybe they can bend it because Worf was the first to go to the Academy, but hopefully they don’t do that.
It depends on how long after DS9 that this series takes place. The Klingon’s and the Federation grew very tight during the Dominion War, even Chancellor Martok was excited that he’d have a Federation Ambassador to go “targ hunting” with, Worf being Ambassador. If that’s the case, Klingon’s may have entered the Federation Academy soon thereafter not in droves, but at least in a trickle.
EDIT: Additionally the Federation could implement a Klingon Officer Lateral Transfer program wherein Klingon Officers are allowed to enter Starfleet through an expedited Academy after the Dominion War.