As long as the headset is totally free, though maybe a bit slow you're OK.

However, any binding, even very slight binding can make the bike a bit harder to handle. Riding a bike involve countless tiny steering corrections on a continuous basis. These are controlled by your cerebellum and you do them with the same level of consciousness given to tasks like walking or eating ---- namely none.

If the steering is sticky, then you have to overcompensate to make those tiny corrections, and the handling becomes jerky, as if you were drunk.

So, you want a headset that's free enough to respond immediately and precisely when you ride no hands and steer by leaning the bike. If it meets that test, all is OK, if not, back it off a hair.