This is my personal experience: I volunteered throughout high and college and beyond. When I decided to attend med school, I got a position as a hospital tutor (as a volunteer). It was fantastic experience because I came into direct contact with patients. The interviewer I had at my top choice made a big point of asking about my experiences there and was very impressed. He mentioned that it sounded like I had a lot of responsibility for someone who was volunteering and I agreed since there were others who were paid for the job I was doing for free. At the end of interview, when I was asking him about the admissions process, he said interview at the school was important and he said mine was a good example of a great interview. I think the fact that I showed him some real clinical experience helped to to get me in despite having only middling numbers (as compared to everyone else they interviewed).
Now, not all my friends who got into med school volunteered as much as I did. One friend got into Harvard with almost no service work but she did have great stats (40+/4.0, tough major, top school, research). Another friend also had good stats (30+/3.5+) but very little in terms of volunteering OR clinical experience. She had a harder time getting in, in part because she applied to only top med schools, but after a year spent teaching kids and applying to lower tiered schools, she made it in.
Just from these and other friends' experiences, I have come to the conclusion, barring great stats for the school, getting clinical experience OR volunteering is a must. As in, if stats won't pull you in, then you have to make sure you have everything else they look for in a candidate, including having the clinical experience. Volunteering is not as important (in my mind) as getting some experience in a hospital setting. But doing clinical work would help adcoms to see that you didn't just pick medicine for superficial reasons (income, 'helping people', etc) but that you know the actual environment you would be working in. Volunteering allows you to show compassion, or at least experience it. Both help you to make better docs and/or get a better feel of what it's like to be a physician. Although not doing one or the other is not going to bar you from med school, it may put you at a 'slight' disadvantage. Since the OP said they were busy with work etc, adcoms may give some latitude for real life intruding. But I highly suggest that unless the OPs stats are very good, get some hospital volunteering under your belt if you don't already have clinical experience.