Should the bit in my impact driver have free play?
It's normal

If this is an impact driver (see below)



then it uses a 1/4" hex chuck. Most use a simple ball-detent system to lock bits in place, which allows for some slip, especially forward and backward.

If you got an impact wrench (see below)



then it would be a problem, but if you were getting an impact wrench, you likely wouldn't be asking this question.