Yes. You must check the Right to Work for all applicants, including volunteers.
What Home Office guidance says
According to Home Office guidance:
You must carry out a Right to Work Check on:
Paid employees, and
Volunteers
You should treat volunteers the same as paid staff for the purposes of Right to Work checks.
Civil penalties and volunteers
Whether you would receive a civil penalty for allowing someone who does not have the right to work in the UK to volunteer is not something the Home Office can confirm in advance.
In this situation:
You should seek independent legal advice that is:
Specific to your organisation, and
Specific to the particular circumstances of the volunteering arrangement.