You definitely can do that. Amtrak has a very loose no change fee policy, so just call 1-800-USA-RAIL (Amtrak’s main number) and ask them to *modify* your ticket to a Roomette. I emphasize the word “modify” because a lot of Amtrak agents don’t really know what they’re doing, and if you just use the word “change”, for example, they may cancel your reservation and rebook you, incurring a fee.
However, though you definitely can change your reservation, I would really recommend just booking it all at once right from the start. a couple reasons: Since sleeper prices fluctuate depending on remaining availability, the time of year, and how far out you are booking, by starting with coach and then upgrading later, you run the risk of ending up having to pay significantly more for your upgrade. Whereas if you pick and choose your dates based on what sleepers cost, and then book it as such, you’ve got much better odds at a cheap(er) upgrade. Does that make sense?