Just a word of warning - being on student council can be a very time-consuming extracurricular, especially if you are looking to be president. At least at my institution, there is a rather large budget to balance and distribute, activities to plan, elections to run, meetings to be had with both the med school council and the University student gov't organization, lists to organize, people emailing you constantly for money/advice/complaints/who-do-I-go-to-for-this/can I advertise my cause at your next meeting, etc. Just making sure each organization got their check took several acts of congress, mostly because some people don't understand/don't want to follow directions, and it is up to you to make sure that they do. You will be stressed and annoyed and overwhelmed a lot of the time, especially if your other officers are people that you don't trust or work well with, or if they go behind your back and talk to other student organizations about your business. I experienced a bit of the latter, and it was pretty obnoxioius. The president is also the one who acts as a point-of-contact, so that person will receive all of the emails and will have to go to all of the meetings, while the other officers don't have as much responsibility.
I have no idea how much it would "help" on a residency app. I took the position because nobody else really wanted to step up and do it, I like being a leader, and because it was an opportunity to work with people I liked and respected. Had I known just how much work was involved, how many meetings and planning sessions I had to go to, and how difficult it was to get every medical group to play ball, I probably would have thought twice about signing up. There were parts of the year where it definitely cut into my study time and probably affected my performance. By the end of the year, I felt like we had accomplished what we needed to do, but very little else. All that headache for a little 1-liner on my residency application? I guess we'll see. I don't think it's going to matter very much.
I'm not saying don't get involved. Just think long and hard about what kind of committment is expected of you.