If volunteering truly is part of your identity, then you will find a way to work it in. Community service, being an active part of the community I live in, and freely giving my time are important to me. I've volunteered in different capacities over my 5 years of doc school. I started real small (a few hours a month) and as the years progressed and I found my rhythm I slowly increased my hours. During this, my 5th year, I've volunteered about 15-20 hrs/month.
Keep in mind I carefully choose volunteer hours which would feed my soul, strengthen my vita, and enhance my clinical skills. For example, for several years I've volunteered about 4 hours/month with a community organization which holds monthly community meetings (caucusing, they call it) facilitating dialogue about systemic racism and ways to break down racism within our community. For me, even though my academic program is strong in this area, we're kind of isolated in the ol' Ivory Tower. This group gets me out into the community talking with folks with very different life experiences than most of my doc school colleagues and professors. A little more than two years ago I began volunteering on an as-needed basis with Physicians for Human Rights' Asylum Network where I am a student clinician and translator. I conduct clinical interviews in Spanish, administer Spanish-language psychological assessments, and help with report writing. Finally, one year ago I began spending about 12hrs/month with a hospice organization. Twice a week I co-lead a support group for grieving teenagers and one day a week I provide companionship services to hospice clients.
Every interview I've had so far has asked about my volunteer experiences and we've "gone somewhere" with that line of conversation. Every volunteer organization I'm with also has had training and some sort of mentorship/supervision. Will they help me land an internship? Maybe. Was I busy during doc school? Yes. Did volunteering hold me back somehow? No way, it enhanced my experience and, I feel kept me in touch with those outside of academia.
If you enjoyed it during undergrad and found the experiences to be life-giving, then you will find a way to give your time during grad school. And I believe you will be a better clinician for it and a more desirable candidate.