Selling a non-fiction book based on a proposal alone happens all the time, actually. I was unpublished, and I did it -- and I was told by both my agent and publisher that my proposal was great, and the sample chapters I submitted sealed the deal.
So to answer your question: no, you don't have to finish the book before you start querying agents. In fact, one of the beautiful things about non-fiction is that you CAN pitch the book before you actually write it, provided you've got a compelling proposal. Part of that proposal, of course, includes platform, so you've got your work cut out for you there, as others have said.
Having said all that, I'd definitely keep poking and prodding and polishing that proposal (including the platform!) Good luck to you!