Yes, you can play solo, manage the sub from any position using a menu of the controls, similar to many of the previous subsims like Aces and Silent Hunter.
You can play solo yet still benefit from wolfpack action, here's an example how:
You can start a mission and password protect your U-boat so no other player comes into you boat. Once the mission begins, you initiate locating and stalking the convoy. Other captains may see your game and elect to join the wolfpack in other U-boats. They cannot speak to you vocally, because they are not in your sub, but as you are playing you may hear the beep-beep-beep of the wireless telling you another U-boat is hailing you!
So then you can read his message, much like a real u-boat commander would have done and if you wish, reply with your strategy on attacking the convoy, point out where the escorts were last seen, and work together as a wolfpack.
Best part, if the other players come and go, if they are any good or not, etc it does not really affect your game. You can still play solo.