In other words, it's possible to have a lower signup percentage, but more total signups.
I totally hear you that it sucks when you know people try your product but leave without signing up, and worse still you have no channel to ask them why. Users exploring a public demo have shown real interest in your solution to problems they have, and while they're exploring (especially if the demo is somewhat guided) there's a very natural opportunity to begin a conversation without requiring a signup. Ask for feedback (via survey, olark chat, quick submit comment form, your contact info...), offer to email product updates or tease future enhancements, show you twitter feed, etc. Moving registration downstream doesn't have to mean you can't learn about potential customers.
Not to say this will never work, but it's definitely not a panacea.
But there's NO reason to make people create a new account. Everyone hates making new accounts, and there are a zillion identity providers out there, from google to facebook to twitter to linkedin to github to yahoo (ad nauseum).
And even if it's too much work right now to configure your application to accept third party identities, you can still "sign-up" users by requesting an email address, letting them straight into the application, and then email them a URL with an embedded identity token that allows them to pick up where they left off.