If you can get it, and if you are willing to do it, an MD/PhD projects you into a much better career path. Not necessarily because you will be better trained for research (some might argue the opposite), but because having both degrees 1) leaves your options VERY open 2) puts you in greater demand 3) gets you paid better and, most importantly 4) makes it easier to get grants initially. PhD's are, for better or worse, a dime-a-dozen these days, and many never leave the position of post doc. There is simply a greater supply and less demand for that degree alone. I just read a great article that was from a link somewhere in the sdn forums that highlighted the troubles that PhDs are having moving past post-docs, getting grants, and getting paid. Often, unfortunately, these highly trained and very capable people are basically used as gifted underpaid techs by their PIs...which is a horrible travesty, because many of these people are the most talented, intelligent scientists around. A PhD is still a very impressive and respectable degree, they are just suffering from a basic supply/demand issue.
That said, getting in to an MD/PhD is VERY competitive, as anyone here can tell you. You truly need to be committed to a career in medical science and need to be able to project a career path and rationale as to why they should pick you (they will be fully funding you, so they want to be 100% sure you are the real deal). Add to that a long list of research experience, hopefully some publications, clinical volunteer time, and some personality always helps. It is also a very long and strenuous pathway, and my impression is that about half who start this way become disillusioned and burned out before the end (based on people I have spoken to). It basically entails 7+ years of school + residency + research fellowship (or a fast-track research fellowship that will run ~ 5 years), and ends up taking a minimum of 12 years before you are out and working.
I am not aware of any bias to accept UGs from the school. In fact MSTPs (NIH-funded MD/PhD programs) seem to be the only programs that really don't care where you are from, but that really go after applicants based on qualifications and research direction. If you really want to work in biomedical research and are not daunted by the time commitment, I personally think it is the way to go.
I hope this was helpful, and if you have any other questions, feel free to PM me.