I understand there would be no advantage to do so but was just wondering if it's allowed. Also has it ever happened?
Yes it's allowed, and yes it happens. Here's an example.
Can you make a free throw off the backboard? I understand there would be no advantage to do so but was just wondering if it's allowed.
Also has it ever happened?
Rule 5 - Section I - a of the NBA rule book states:
A legal field goal or free throw attempt shall be scored when a ball from the playing area enters the basket from above and remains in or passes through the net
Rule 4 - Section I - c states:
Five sides of the backboard (front, two sides, bottom and top) are considered in play when contacted by the basketball. The back of the backboard and the area directly behind it are out-of-bounds.