Doesn't connect to a yard which is one major problem in my opinion, meaning T/O's will have to go from CI via West End. Most lines have an easy connection to their yard. Look at all the lines and where their yards are and you'll understand.
If this would be possible I would terminate it at Chambers via tunnel and have it turn back there, because people can get on in both directions, and then you don't have to make a switch or track where there isn't one. In addition there would be less tracks to share with other trains and less merges.
In Brooklyn I would run it via West End, instead of via the R the entire way. That way it has a direct yard connection, and more access to 4th Av local stops than Sea Beach would, although Sea Beach is also a good contestant due to higher Sea Beach ridership.
The better option would be extra service that short turned at 57th St. It would provide downtown and midtown service, and a possible future SAS uptown service. With that you still run the no-yard problem, but it shouldn't be a big deal as the line is still mostly part of the . If this were to happen however, I would send some trains via Broadway express to alleviate crowding. This seems best as a rush only service. However the downfall is the lack of connection to the Nassau St line.
All in all, this brown R idea has some potential, such as more 4th Av local service. However, I find a line like this would have very low demand of ridership because it only connects to Lower Manhattan. The better idea, mentioned above would be the short turned 's to 57th, however it also has it's downsides.