A bankroll is an amount of money, that protect a winning player from going broke due to short term variance. So in order to even begin thinking about having a bankroll, you first need to be a winning player, which require study and practice. And while playing freerolls does obviously give some practice, its far from ideal, because people play very differently in most freerolls, and you are also a slave to the freeroll schedule. You cant just sit down and play for 2-3 hours, whenever you have time.
So while it might be possible to eventually reach stakes, where
real money is at stake, without ever depositing a single dollar, the real question is, why on earth would you want to do that? You are just making your chance of success way smaller, than if you start with even just a small deposit of $50-100 and then go from there. And if its a question of finding those $50-100, then for sure there are much faster ways to do that than spending endless hours grinding for pennies in freerolls.
So the much more relevant question to ask is the following: "Can you create a bankroll by working at McDonalds". And the answer to that is absolutely yes. Its definitely possible to earn $50-100 working at McDonalds, deposit it to a
poker site, start playing either 2NL cash games or $1 tournaments, and then go from there. And this is a far more efficient use of time than playing freerolls.