I'm afraid I join the majority in saying don't invite her. I think a wedding would be a very high pressure event for an alcoholic with no plus one, seeing a friend and contemporary get married, with everyone celebrating couples, families, relationships, and looking well scrubbed up and generally emphasizing the good in people's lives.
High pressure if you are not in that same place with life or relationships, let alone adding a bad relationship with alcohol and the accompanying fall out for everyone else.
I think it can sound very mean and not inclusive, until you've tried to control or limit the destruction an alcoholic can do. It's really upsetting having events ruined by someone who then can't / won't be held responsible and quite possibly can't even remember what they did.
When younger there were 2 people with alcohol problems in our very close friendship group. We couldn't go out anywhere as the evenings would be 'carnage'... But not in a good way, and the 'amusing' tales of extreme drunkenness just got less and less funny, and I was constantly being stood up / left in clubs / on deserted streets/ unsafe parts of the city or other dodgy situations for a young woman to send up in. And then the aggression, fights with strangers, and us... It became miserable and it was years before I finally realised that they put the alcohol before anyone and anything. All my strategies for changing the result of each time we met failed, mid morning or daytime meets still involved alcohol, staying in became unpleasant with fists through doors, broken stuff, storming out etc. Sadly it broke our friendship group up, and I learnt self-protection very belatedly. I had a more recent experience with an alcoholic who lied her way into a very responsible position, and although it took me still too long to work out what was happening, this time it was weeks, not years before I took steps to protect myself...
I think there comes a point when either someone takes responsibility for their own issues, and therefore gets loads of support, or other people have to start protecting themselves. It's a sad situation.