If it's available, you can always (or at least should be able to if the Conductor wants to do the paperwork involved) upgrade onboard. (The only exception is on the Auto Train.) The upgrade cost is the difference between what you paid and the low bucket for that type - with a minimum increase (of IIRC $50).
So really, the only time this technique will result in a room at a significant savings is when you decide to take a short-notice trip and the sleeping accommodations are mostly sold, hence only the highest buckets are available. If you have the ability to plan sufficiently far in advance, you get the low bucket as a 'reward.' Waiting until you're on board runs the risk of a disappointment -- full train or only expensive full rooms available or worst, you get a cheap room but have to give it up halfway because someone is boarding mid-ride and has reserved that room. Come to think, in that latter case the conductor might refuse to let you have the room anyway.