Can I use a pick in adventure mode?

Not yet. Adventurers being able to dig or change the landscape in other ways is on the list of future things to do, but the amount of data the game would have to keep track of to support it is astonishing. So it's not really going to be implemented in the foreseeable future.

You can use it as a weapon, though; it uses your Mining skill in place of Sword, Axe, or Hammer, but it's otherwise not that great a weapon so there are usually better choices for adventurers. Picks work okay as an early weapon in fortress mode because fortress dwarves often have extremely high Mining but no other weapon skills.