What is the point of the Tankard?

There are no real benifits of it. You could technically say you could use the vomit to your advantage by blinding enemies in a PVP fight but other than that it is just a bit of fun to be had on those long voyages across the water.

Tried playing some tunes after drinking, it's very entertaining :)

There are a few achievements that can be gained by drinking:

• I'll Drink to That [5G]
  "Nothing says being social, like crews drunk down the local."
• What Shall We Do With a Drunken Sailor? [10G]
  "A tankard or two may make you blue, have a few more and you will surely spew."
• A Titanic Ensemble [10G]
  "A pirate once said that when you are sinking, playing some music is more helpful than drinking."
• Tactical Chunder [20G]
  "There is an old saying that to win a sword fight, a tactical chunder will ruin their sight."