Some people say yes. I say no, at least not at the beginning of the process.
True, it's more fun if you care. The best fun out there. But fun isn't the only enjoyable aspect of writing. There's also challenge. And there's a lot of challenge in starting to write a story for which you don't give a flying fuck at a rolling doughnut.
I guess I should define care here. When I care about characters, I usually mean that I like them, and/or want to see them conquer their enemies, achieve self-actualization, whatever. If I wouldn't necessarily want some of them to be my everyday buddies, they would be interesting people to meet at a party and then back away from, slowly. Care can also mean I want to see them lose their evilly-gotten gains, be insulted, or simply get killed gruesomely.
Trying to find reasons to care about a character, now there's a challenge. What could Blank Slate possibly do that would make me love him? Or make me want to stick an icepick in his ear? And why would he do that? And how will he go about showing it to the reader? And who will get in his way?
See, instant story. Because I didn't have a character I automatically felt something for.
ETA: I do, sometimes, have characters I like ahead of time. But by no means always.