I would guess it would depend on the hotel. If we are talking a unique hotel, say the Whitcomb in Frisco or La Pavillion in New Orleans, advertising might do something. But often when I set out on the road, I shop for a hotel that meets one of a list of national brands I know I will get a good nights sleep, and then go for the lowest price. Days Inn is not on that list- it is far too inconsistent. Advertising is rarely worth it for chain hotels- because they aren't chains. They are franchises, and they are paying for the basic advertising of being in that brand.
Smaller hotels have a limited market. While I am on vacation, I like staying in oddball, but not high end, older properties. I also know that a lot of people would never set foot in such a hotel. They are never cheaper than Motel 6 or Super 8, and with those, you know what you get. It isn't much, but you can sleep.
The fact of the matter is, I have no idea what the price of this program to Amtrak is. I don't remember of T&R people get sleepers. Meals, I hear they get here. If you are talking about a summer Zephyr, it probably costs well north of $500, including sleeper, hotels, meals, and so forth a run. Thinking outside the box, frankly, is often a dangerous thing for a large organization to do.