Yes, but you will miss a few things and probably get a little frustrated. But there are two guys who will teach you and one has a practice area. Use them just like you would your fighting skills and you can level up. Doesn’t take much before you can open most locks. There will still be some that will be impossible for you though.
The lock pick game is really hard with a controller. I actually played the game with a controller, but switched to key board to open locks. Much easier.
It is also worthwhile to fight in the contest arena (forget what they called that in game). You will get your ass handed to you at first but you can skills by doing it and eventually you can win.