People who die in Soul Society being reborn in the Human World is established in the manga. ANd based on what we know, no it doesn't make Ichigo Kaien's reincarnation. We do not know how long ago Kaien died, but it was never stated to be before/around Ichigo was born. Also, Kaien's body was merged with the Hollow and reconstituted itself in Hueco Mundo where it was absorbed my Aaroneiro, who was alive and well long after Ichigo was born.