Miravlix: The original question was whether you should take Tradition (and/or Legalism) to get Liberty done faster. The answer is 'No in almost every circumstance'.
If, however, you know that you want 'Tradition, Liberty, Commerce, Rationalism, and Order' in your game, and you don't care the order in which you take your policies, then yes, Tradition/Legalism is probably the fastest opening.
Most people on this thread have assumed (and that assumption has been more or less explicit) that the original argument was whether Tradition Opener + Liberty + Commerce + Rationalism + Order was faster (to finish Liberty) than just Liberty + Commerce + Rationalism + Order. And, as stated above, that is a rather simple question to answer.
civzombie: It would be very interesting to check on Persia. This is something best done with simulation, as the number of variables otherwise gets rather large. That is, unless, you want to ignore Happiness-based Golden Ages?
Re: Amphitheater-based Legalism, the answer is probably still 'no', in terms of finishing Liberty faster by not taking Tradition. Let's say you plan on going Tradition -> Liberty -> +1 Prod -> Settler (settle this and make/buy Monument before) -> (research Drama, probably from GL) -> Legalism -> Worker -> GA -> Trade Route.
This would give you 2 Amphitheaters (possibly, but not likely, with 2 Great Artist slots being worked), and 2 Monuments. This is 3+3+2+2+3 (tradition) + 2 (Liberty) = 15 cpt. Let's add one for GL for 16. We may have 6 more for 22. Now, is this better than otherwise? Well, if you would not have taken Tradition otherwise, that's 2 more policies that you have to 'pay for' with the increased cpt, and it's probably not worth it. This also assumes you burn the GL on Drama and not Philosophy, which delays your NC.
This approach would probably be best for (IIRC) the Songhai, as they _could_ get Philosophy, and get their Mosques rather than Amphitheaters.