No, if one upgrades onboard, the charge for the roomette is priced from the next station stop at the time the conductor is doing the upgrade. So for example if you left out of DC on the Cardinal and asked the conductor to do an upgrade shortly before Hinton, the charge will be based upon the low bucket fare from Hinton to Chicago. It's also important to realize that even if there is a room available out of DC, if you wait until just before Hinton for example, someone else on board may gobble up the last room. And I'm not sure that the conductor would hold it for you even if you ask early on, since he'd be cutting into Amtrak's revenues by not selling it to someone whose going to pay to move immediately.
I've never heard of anyone however asking to downgrade the next morning and I'm not sure if the conductor would want to do that, much less if he even can do that. So if you really want to ride in a sleeper for just a portion of your trip, you'll need to rebook it into a three segment trip. The first and final segments you'll book in coach, the middle segment in a sleeper. That of course would net you three tickets and since they'll all be for the same train, if you're a member of Amtrak Guest Rewards, you'll get screwed out of points since there is a rule that prohibits one from getting multiple points from multiple tickets for the same train.
Finally, I'm not sure that you'd save all that much money by trying to do something like this. Doing an onboard upgrade as soon as you board isn't going to cost all that much more than playing this game, even if the conductor can do an upgrade and downgrade.