Im making a couple of assumptions here. First is that when you say the screen is shot, you mean physically broken so that it wont work. The second is that you want to mount the sd card so much hat you can get the stuff transfered.
If these are correct, then the answer is yes. But it requires adb, which is a command prompt program. If your goal is to get things off of the card, a much simpler way is to buy a micro sd adapter from any big box store for 10-15 bucks. If my assumpfions are wrong, please let me know and ill see if we can get something figured out for you.
sent from my gutted continuum. courtesy of imnuts adrynalyne and trailblazer