Ja
Stöd för din plan finns precis i kärnreglerna, MM (s.141):
A genie usually retains no connection to the soul that gave it form. That life force is a building block that determines the genie's form and apparent gender, as well as one or two key personality traits. Although they resemble humanoid beings, genies are elemental spirits given physical form. They don't mate with other genies or produce genie offspring, as all new genies are born out of the same mysterious fusion of spirit energy and elemental power. A genie with a stronger connection to its mortal soul might choose to sire a child with a mortal, although such offspring are rare.