No.
Applications and data stored within the Private Space are not visible to enterprise administrators, this follows the existing premise set with the parent profile in a work profile (company/personally-owned) deployment. If this is an organisational concern, application policies can be set for company-owned work profile deployments.
This may sound contradictory to Are Private Space applications truly hidden?, however this is because the EMM agent runs within the work profile, which is intentionally restricted from visibility of apps outside of it.