Organized religion has flourished in human history chiefly because humans are very social entities, concerned with being part of a group, and constantly fussy about how the group perceives them. The Sharing took advantage of the basic factors that motivate 'successfully organized' religious groups - that is, the obsession with status, popularity, group/caste/rank... - and skipped over the gory details of creating a belief system, instead just going straight to the heart of human interactions by implying that it's a vaguely bad idea to not be part of the Sharing.
In all likelihood, they could have expanded their ranks by making other branches of the Sharing in other parts of the world, with a more relgion-based focus... but for that geographic region, with so many teens in a small area, conveying to their extended families the feeling of being scrutinized... seriously, we think the only thing that would have made them MORE successful would be if they started the invasion in Boise and Utah, with the most powerful members of several Mormon churches. You want social pressure to conform, go there; you'll be wowed.
Anyway, basically... the Yeerks could use religion, and it would have worked scarily well in parts of the world that are utterly controlled by a specific religious group... but for areas under less-specific influences, it works as well if not better to just play directly on the human urge to conform to the herd.