In this case I'd say yes, use Lib for Democracy. It's not 3 extra turns on Emancipation that make big difference, but the Lib's own benefit -- Free Religion for +10% research, and Free Speech for +2 commerce from towns.
With this benefit you'll tech toward Rocketry a lot faster, and most likely save more than 1 extra turn. That is, you won't save 4 turns on Rocketry, but you'll start researching it, to say, 6 turns earlier. So, you'll finish it 2 turns earlier.
In my current best submission as Peter I used Liberalism for Computers. In G-Major 12 as Huayna I used it for Democracy.