Can I install a Sharkbite shut off valve with only a half of an inch of copper to connect to?
No.  You will need about 1 inch.  It will hit the stop at about 1 inch and slightly (very slightly) pull out after it hits the stop.  This is something that you don't want to mess with because if you don't have the correct length the bite action won't take.  Good thing is unlike a bad solder job on copper you will notice that you didn't hit the stop right away.  

Instructions here.