From all the people I've spoken to, including guys who have been through FSP and from guys who work at FSP, getting some flying experience is almost essential, but not entirely. No one will come out and say "You NEED flying experience", because the official stance is you don't. Like in the ad on TV, the guy says he became a Hornet pilot with no more flying experience than counting the times he'd flown in Jumbo's as a kid. Which I'm sure there are lots of pilots who have done it that way, because they show a genuine aptitude and talent for flying and learning to fly.
Getting experience, even if it's only a few hours because you had to scrimp and scrap and work ****ty jobs and long hours to afford it, shows you're motivated to fly. I've spoken to guys who went with no flying experience and were asked "Why do you want to be a pilot?", they respond with something like "It's what I've always wanted to do". The board can only then ask "Well, how do you know? Where's your proof? You've never flown an aircraft, how do you know you want to be a pilot? Go away, get some hours, show us you want to be a pilot, and come back."
So the long and the short.. getting some hours shows you're motivated. And it'll really tell you if you really do want to be a pilot or not. You never know, you mightn’t enjoy it.