There is no "drunk and disorderly" in New York and no cop would use that phrase.
She could be arrested for Disorderly Conduct ("dis con"), a violation, but generally would not be. For that she would most often receive a criminal summons which would require her to appear in court at a later date. In many cases that would be issued right on the street, like a traffic ticket. She could also be brought in to the station house and released with a summons.
If she was too drunk to care for herself, she would likely be sent to the hospital as an aided intox, sometimes with that summons in her pocket, most often not. You're really not supposed to summons a drunk. Drunks are generally not arrested in NYC because nobody wants to be stuck with them. It does happen, a lot, but not if it can be avoided. There would usually need to be another reason (criminal offense) for a custodial arrest.
If she simply "slapped" a cop, that would be Harassment, a violation. You say she did this "while detained." I'm not sure what that means.
If she slapped a cop after being arrested, while being printed, for example, she would probably get some wall to wall counseling and that would be the end of it, no additional charges. By then they would know who she was anyway.
If she did it on the street, she likely would get knocked down and then arrested. In that case, today she'd catch an Assault 2 charge. In the '70s? Probably Assault 3. In either case, a Resisting Arrest as well.
And yes, your outcome is reasonable.
In the '70s she'd be unlikely to get mandatory rehab, especially as a celebrity. Today she'd probably receive an ACOD which is an adjournment in contemplation of dismissal, that is: don't get collared for the same thing for six months or a year (whatever the judge decides) and the whole thing will be wiped away.
Anyway, that's off the top of my head.