I know Americans call him St Patty, but it's St. Paddy'... it's from the Irish version of his name, Padraig. Patty is the diminutive of Patricia.
It really doesn't matter which you do first. There won't be a great deal of difference in the final outcome. If you do decide to smoke first you will benefit from double bagging to sous vide, otherwise you may finish up with a kitchen smelling faintly smoky.
I'm more inclined to sous vide first and then smoke. For corned beef I soak the meat in clean fresh water for 4 to 6 hours to remove some of the salt before bagging it and cooking sous vide at 60C/140F for 24-48 hours depending on the cut. From there I usually just sear and serve.
If I'm going to smoke something post sous vide I'll shock chill and refrigerate. On the day of the event, I'll smoke the meat back up to the desired internal serving temperature, usually a bit higher than the cooking temperature for security sake.