Yes. The effects of Prone: Prone troopers have a Silhouette (S) value of 0, that is, the equivalent height of a base. While in this state, troopers have both their MOV values halved. While Prone, troopers cannot Jump or Climb. Prone troopers that are the target of a BS Attack declared by an enemy from a lower position than them will benefit from Partial Cover MODs against that attack. This state does not affect Automatic Special Skills or Automatic Equipment, except when explicitly stated in their description. If you can still see the target, you can declare BS Attacks just fine. And you can fight in CC just fine, too.
