As long as you have an individual Premium plan (or a Premium plan provided by virtue of being a member of a paid Organization plan), then you will be able to generate TOTP codes for any items that you have access to (items in your individual vault, as well as shared items in organization vaults).
There is a feature request here:
However, I’m not sure that I understand your use-case. You mention an “organization”, but if it has a “large…user base”, then you must be talking about the volunteers using Bitwarden for their own individual logins, not for shared logins belonging to the organization. In that case, could the volunteers not just use the stand-alone Bitwarden Authenticator App?