More than you would think. I was one of the people who grinded my ways from freerolls and now sit with about 700 bucks. Not a lot of money by any means, but I'm a bankroll nit .
Think of freerolls as free training. At least in the freerolls you will learn a few postflop betting basics once most Johnny all-ins are gone.
I still wouldn't recommend building your bankroll from nothing playing in large freerolls. On full tilt, I won my first two bucks from UK freeroll (A field of about 1000 people, but I believe at least 200 of that were sitting out). I didn't have much luck in Pokerstars
or Absolute freerolls where a large number of entries means infinite variance. Once I won that two bucks the skills I've learnt from freerolls gave me a head start in micro tourneys and SNGs.
To conclude, don't underestimate the usefulness of freerolls, but don't count on them being able to provide quick few bucks to kick things off either. I had spent at least 4 months splashing around in freerolls before I had a decent bankroll to no longer rely on them. My advice is to play a few freerolls to make yourself comfortable with the fundamentals, then deposit.
GL at the tables