Pros
It's a full time federal job. Can potentially lead to higher grade positions w/in SSA or elsewhere. Despite what others may say the skills learned as a BA are useful in other positions throughout the federal government. You learn to research and analyze policy, screen, and process cases. That directly correlates with Legal Administrative Specialist, Retirement Services position at OPM in D.C. The training, expectations, and nature of the work literally mirror one another. That particular job goes to a GS 11. The Department of Labor, Department of Commerce, Merit Systems Protection Board and other agencies have positions where BA skills will be helpful. The job position is policy oriented, so knowing how to find policies in PolicyNet is helpful if you happen to obtain employment at DHS agencies such USCIS.
Cons
A lot of the cons have already been posted here. I won't regurgitate them. If you have this job currently, just try to stay on top of the learning, don't overthink it, and remember to hit control F to find answers in the lessons for your exams. Favoritism does occur, here. The lack of flexibility and rigidity with the time was the biggest con for the program for me. The class I was in was also moving at an accelerated pace and several of the instructors were biased and shared biased information about students with one another. FYI, OPM writes guidance for many programs like SSA's BA program, but they don't follow those rules themselves. I happen to be in OPM's training program which is similar to the BA training, and it is VERY VERY laid back.