The phallic nature of the Genesis device is likely a coincidence.
First, I should say there is very little information about the Genesis device prop itself.
Although there is a photo (above) of producer Rob Sallin standing beside the prop shortly after filming was completed on The Wrath of Khan, not much is known about the commissioning of the prop, and there has been some discussion on various message boards regarding the design and current whereabouts of the prop. (Its whereabouts seem to be unknown.)
In particular, the prop may not have even been designed by The Wrath of Khan 's on-staff prop designers. The device's activation console, for instance, was rented from an outside prop firm (see here, for example).
In contrast, there has been considerable information released about the Ceti Alpha eel props, for example. (Apparently, they were originally supposed to attach only to the neck of a victim, but this was seen to be too similar to things appearing in other science fiction works. Soon after, Sallin saw a slug on the ground and daydreamed about it crawling into an ear. See here.)
At the end of the day, I believe the phallic nature of the Genesis device to be a coincidence, and that its shape has more to do with the initial conception of the Genesis project.
I arrived at this conclusion by putting together some known facts about the evolution of the film's plot. It is known that, in an early version of the script for Star Trek II: War of the Generations (the original title for the film), the Genesis device was called the "Omega System". (An episode of Voyager gives a nod to this by referring to the "omega particle" and the "omega directive".) It was originally intended to be a powerful new weapon developed by Starfleet. However, it was eventually felt that Starfleet should not be portrayed as being too interested in weaponry, and so it was decided that the Omega System would be given a noble purpose that could be perverted in the wrong hands — hence, the Genesis device was born. (See this io9 article.)
I suspect that the initial idea of the Genesis device as being strictly a weapon stuck in the minds of producers and designers, who gave it a torpedo-like shape — even though this shape is not necessarily required for its actual function, as Khan demonstrates at the end of the film. (Its shape also plays into Kruge's conclusion that Genesis is a weapon in The Search for Spock. He refers to it as the "Genesis torpedo".)
So, as @DVK mentioned in the comments below the question (channeling Freud), sometimes a torpedo is just a torpedo.