in regard to Hyperledger Composer yes, its possible, as it sits atop Hyperledger Fabric as its incumbent blockchain where the ledger sits and as you know Fabric is a permissioned blockchain platform.
There is an example here -> http://www.goverticalworkshop.com/resources/how-to-create-a-decentralized-application-running-on-hyperledger-fabric-network
(it has sample links to resources it uses but I do notice that some commands (eg composer network deploy
need updating, but can see similar from the docs
Sorry you'll have to ask APPII if they're using private or public blockchain or do your own research. Given that they are partnering organisations as verifying institutions/partners and interacting with joe public to upload their CV, so that its constituent claims/artifacts can be validated/verified - the use case is hybrid (it would seem).