Of course...immediately after I post this I found a partial answer.
Commissioner Paul Tagliabue's authority is detailed in the league's policy on substance abuse, including alcohol. Punishment for the first offense generally is a fine of no more than $20,000, according to the policy, with more severe consequences for repeat offenders.
"Discipline for a second or subsequent offense is likely to be suspension, the duration of which may escalate for repeat offenses," according to the policy.
The league requires counseling for players with substance abuse problems.
It sounds like it is considered a violation if it results in a conviction and a suspension is considered for multiple offenses.
"I'm normally not a praying man, but if you're up there, please save me Superman."
- Homer J. Simpson