I really doubt that they'll make Carol an alcoholic in the MCU. Tony isn't even officially an alcoholic in the MCU (they kind of adapted elements of the Demon in a Bottle story arc for him, but without tying anything to alcohol).
In the comics she is. In the 90s Avengers run (Kurt Busiek as writer, I think) she started drinking a lot and eventually she tried to stop a bad guy while drunk. It did not end well, and I'm pretty sure she got kicked off of the team for awhile. Its brought up every so often, the last time I saw it mentioned was last year during the Civil War II event where she and Tony accidentally meet at an AA meeting while they're on opposite sides of the conflict (they'd both gone to an out of state one trying to avoid each other).