I've been looking into this lately too and haven't found any concrete studies, which is why I am about to establish a new website focussing on critically-endangered species that are not so "charismatic". I'll post the link here when it is live.
In 2008 Barbara Clucas, Katherine McHugh and Tim Caro published an interesting work on flagship species featured on the covers of ten representative US conservation and nature magazines (see attachment). I think this information could be useful to partially answer your question. Best regards. RAF