By everything we know the answers are both "no" and "no." It will not have a soul, and it will not reach heaven when it "dies."

Humankind became "a living soul" when God breathed the breath of life into him (Gn. 2.7). The presence of intelligence neither requires nor assumes a soul (dolphins are intelligent, but we don't theologically consider them to be ensouled. Nor does consciousness or feelings (earthworms are conscious and obviously feel pain, at least the one I tried to dissect in biology class seemed to!) necessarily betray the presence of a soul. Even though AI may be given a mechanical body and be programmed to learn, even to feel (though the possibility I would think is quite remote, if at all possible, and possibly impossible to prove), ensoulment was a specific act of God. As far as we know, we can't evolve into having a soul, necessitate it by consciousness, or bring it about by our own efforts. As far as we know, theologically, even though many organisms have consciousness, feelings and intelligence, only humanity is ensouled.

It's a hypothetical question. Assume that we will, some day, create a true AI. By that I mean AI that is conscious, that have feelings and is very much like a human. Will this intelligence have a soul? Will it reach heaven when it "dies" (shut down or is broken in some way)?