It's not like applications are a 40 hour a week job... most people on this forum (myself excluded, I didn't get mine in til mid August) have their applications ready by June, so I don't see a reason to sit around doing nothing for the next 3 months. Secondaries generally take about 1-2 evenings each (depending on the number of essays), so those shouldn't be much of a worry either.
It's definitely important to take time to study for the MCAT, but assuming you've got a decent understanding on the background, it should doable in about 2 months assuming you study for 2-3 hours a day. I think a lot of people's MCAT study schedules (8 hours a day every day for multiple months) is overkill. The MCAT is less about what you know and more about applying it (though it is required to have a good grasp of the material).
To directly answer your question, many people asked me about what I had done during that summer but that may have been because it was a significant research experience and one I enjoyed talking about. You might not be asked any questions about it, but I don't think a part-time job or lots of volunteering (at least 20 hours/week) is too much to handle, and would at least cover you in case you do get asked about it.