Is it possible to set a collection's permissions to public via either the Node or REST apis?

If so, how so?

You cannot do this on a per collection via node or rest, no.

You can make a business logic script to query the collection and iterate over the returned results, and set them as "gr" (globally readable).   You can read more about acl's over here http://devcenter.kinvey.com/rest/guides/security#entityanduserpermissions

Thanks,