This is a great question, and one I've never really thought about. Honestly, I never thought it mattered, so I've never put descriptions into my domain listings.
As others have mentioned, I do believe it's gonna be pretty hard to get your names indexed and ranked in Google for anything with somewhat decent search volume (even in the couple hundred per month range) just because you put a unique description in there. Does it let you set Meta Title/Description tags? Are you able to bold any of the font? How many characters is it limited to? If the domain had tons of great backlinks or it's an extremely noncompetitive term then maybe. In the screenshot above DAN says it can help you in search engines, but not on their own platform.
I'd almost be more interested in knowing if putting a unique description in there would help you rank higher in marketplace searches. If so, it could help you rank a domain like CheapestHotelRooms for a popular search term like "Hotel" in the marketplace which still probably gets a good amount of searches in a month. There are probably thousands of domains listed on the marketplaces with "Hotel" in them and it'd be cool if there was a way to outrank a bunch of those people. You definitely aren't parking a domain and getting it ranked in Google for "Hotel"...
No big surprise DAN says putting it in can help you get indexed and ranked. I'd put the same thing in there because technically it can help, but for the most part in terms of Google search it isn't going to. You need lots more than just a 300 word unique description to rank in the SERPS for anything that's really getting a decent amount of searches. I'd be more interested in putting unique descriptions in each of my domains if DAN said it can help you rank in DAN searches, because I know probably 99% of the domains listed on there DON'T have unique descriptions in them and I could easily take lots of names and get them ranked for GREAT terms that probably get a good amount of searches each month on the marketplaces themselves.