I did an MSW before going on to a PhD in School Psychology. An MA in Psych does not make you more competitive necessarily. In fact, a lot of programs are looking for intellectual diversity. While not a huge factor in acceptance, having a degree in a slightly related field (MSW, MPH, etc) can give you a different perspective that admissions committees will be interested in. It might give your personal statement and interview a flavor MA psychs might not have. However, this flavor will not overshadow UG GPA, GRE, personal statement, etc.
MSW and similar masters programs will give you both field and research experience. Actually, this is more program specific rather than discipline specific. Make sure your masters program has a hefty and well supported field and research component.
Another thing to consider is what will happen if you don't get a PsyD or PhD. In my area in Texas (and from what I've heard, all of Texas) the LCSW (MSW + 2 years of clinical experience) is WAY more marketable than the LPC. In fact, a search on simplyhired.com or monsterjobs.com will reveal that LCSWs and PhD/PsyDs often compete for similar positions.
Anyway... on to what you get in an MSW...
MSW education is VERY broad. Now, this is both a pro and a con. The pro is that you learn a lot stuff. You get some business administration training (non-profit oriented of course), abnormal psychology, sociological theory, community intervention, ethics, law...SO MUCH! The con is that you don't go deep in these areas. You could personally, but the courses wont. Now, to be sure, you will select a concentration and that will allow you to go deeper in one area. The concentrations are typical micro/clinical or macro/community. Micro will be your concentration if you want to do counseling. However, again, it won't go as deep as the MA Psych. Some people in micro concentration want to work in adoption and CPS so they can't just gear it to all therapy and diagnosing. Macro concentration is more about non profit business/social service administration, community advocacy, and social justice.
You mentioned underprivileged populations. The PURPOSE of the profession is to serve underprivileged populations. Now, does every LCSW work in rural areas or poorer counties? No, but that is the orientation of the profession.
Another thing to consider
The role of social workers in school VS. psych counselors are very different. Some school districts wont hire social workers to be in counselor positions. Some districts only hire LSSPs (School Psychology masters). You need to look into that for your area. Typically, in schools, social workers do a lot more macro stuff. They work with families and students trying to get them resources (tutors for free, free lunch, clothes, etc); basically you hook them up with social services.
Well I hope this helps. Feel free to PM me if you have more questions. I encourage you to ask a clinical psych professor and a social work professor. They can give you more information particular to your area.