If in doubt, offload.
Absolutely no qualms about offloading drunk and/or abusive passengers at my airline. We had one character recently who'd had a few too many in the airport bar, staggered out to the aircraft and, when asked for his boarding pass, declared that he couldn't "fxxking find it." The no.1, deciding he was on very thin ice, allowed him to board but put her head round the flightdeck door and advised us she was keeping an eye on him.
His luck ran out just before the doors closed, when he decided to liven up the no.3's welcome p.a. by doing monkey impressions to his mates. The no.1 swiftly returned to the flightdeck to ask if we could offload him. No discussion - security were called and he was escorted from the aircraft. As he was led back to the terminal, he was still arguing and swearing - which begs a question, if he was like that surrounded by half a dozen security people and a couple of policemen, what would he have been like at 20,000' with two young female cabin crew?
The only thing predictable about drunks is their unpredictability. He might have fallen asleep, but then again he might have got seriously unpleasant. It's not a risk I'd want to take. I would much - much - rather take a slot delay than risk someone kicking off in the cabin whilst in flight.