feasible? ... yes. you can definitely do it, and there are many successful MD/JDs out there. but it will be a lot of work. i am finishing med school and my wife law school, and the combination of the two over a 7 year period would be a decade to forget, imo.
i'll tell you what i know from my wife, as she was interested in it and worked this past summer for a firm doing patent law. nearly all the attourneys in this area had at least a masters, and some had a PhD, in a science major. of course an MD would certainly qualify. those attourneys that did not were forced to take on the non-scientific (read: boring) projects that could get old very quickly. she did not work with any MD/JDs in the patent department, so I cannot comment on the work they would have. but certainly you would work on some very cool stuff.
i think it would probably be best to get the MD first, then go to law school. keep in mind that to practice patent law you must be able to sit for the patent bar, which requires you to have a bachelor of science, and is an entirely separate exam from the regular bar. you also have to take and pass the regular bar. lots of exams in both schools.
again, this is a long road. to answer your question ... yes, it is feasible. can you do it without the MD? of course. mostly depends on how much torture you want to put yourself through.
Thanks for your response. The MD/JD really does seem to be more trouble than it is worth, even though patent law is a very interesting job. The MD/MBA seems infinitely more viable for those who get tired of clinical practice.