rushing a fraternity

I have already used some of my connections to get invited to a few fraternity's rush events but I would like to get to know the other fraternity's to find where I best fit in. If I don't know anyone in the fraternity would it be inappropriate to email the rush chair? To me this sounds like it would make me sound desperate and lesson my chances of getting invited to an event. I know that Old Row probably doesn't reach out to people without connections but what about the New row houses?