It's usually a bad idea to apply without a website because they have nothing to look at. The rest of your credentials must be pretty impressive if you're going to win them over without a site.
Agreed. If a network accepts you as an affiliate without a decent Website, I would be skeptical about that network.
A website is key. Otherwise you will have to show a business plan of how you will bring customers in from offline marketing. Bonus codes and promo codes will be needed to do this strategy.