This is a great resource:
http://www.public.navy.mil/bupers-np...s/default.aspx
This link takes you to the community overview. It documents the current promotion rates for the various administration ratings, as well as career paths.
The bottom line is that the chances to switch to LN are pretty much going to depend on A) Your competence and B) The Needs of the Navy.
Right now the LN rating is at 90% of their FY-16 enlisted personnel. What that means is that if you were qualified and had good reviews, they would probably take you. The hold up there is that YN is currently at 97% manned for FY-16, so they are not really wanting people to go, especially E1-E3 (currently 75% manned)
YN is not a dead end job by any means. It might not be as glorious as say, AO or EOD, but from the administrative aspect each armed service is basically a government Bureau/Department. The navy could not function very well without the Yeoman and Support Corp Officers to take care of all that red tape.
In addition to the LN rate for advancement, you also have the Navy Counselor (NC) and Mass Communications (MC) ratings as part of that same general community.