If a pitcher fake a throw to a base is he considered disengaged? So technically then could he fake a throw to first base?
Faking a throw is illegal when touching the plate ("engaged"). 6.02(a)(2):
If there is a runner, or runners, it is a balk when:
(2) The pitcher, while touching his plate, feints a throw to first or third base and fails to complete the throw;
However, a pitcher not touching the plate is a fielder and can do any normal fielder thing, including feint throws. So once a pitcher has stepped off (i.e., his back foot is no longer on the plate), sure, he can do whatever he wants.
Regardless, I think the answer to the question you intend is effectively no; if the pitcher, while engaged, fakes a throw to a base, that is a balk. The pitcher would have to remove his foot from the plate (at which point no sane runner would be going anywhere other than back to the bag).