No you won't get it faster. But you'll be in better shape when it comes. I really meant fast ENOUGH and not FASTER
You are right that getting it straight is faster. But Piety is so bad at culture that you won't get it SO much faster. And getting it fast will probably ends up being useless when it comes. You're just better off making a very strong empire with slower reformation with liberty and then using oracle to grab the reformation quickly than trying to go straight into Piety and having a weak empire when reformation kicks in.
Another very important thing I've been trying for the current gauntlet is that since liberty allow you to hook luxuries faster and sell some of it, you'll end up with more gold than Piety, allowing you to also ally cultural CS.
Finally, don't forget that reformation is not the finisher, you only need 8 policies not 9. Getting 8 policies quite fast with liberty, cultural CS, Oracle AND faith building is not hard.
I guess you could factor in competition however so it also kind of depends on which difficulty you play I guess.