You may install PeopleSoft on your system for testing and only for yourself. You cannot open service requests for unsupported/unlicensed software.
As Jim said, You may install for self use only. Ideally you should have licensed software to use in every domain.
For business, PeopleSoft license codes are needed when you do a fresh install of a PeopleSoft demo or any other install. You also need this license code when you apply PeopleSoft application bundles and patches or when you do PeopleTools upgrade or apply a patch. If your customer already has a license, you can very well get it from him otherwise your client will have to buy PeopleSoft license from Oracle.
For Licensing, Refer:
Assistant: My Oracle Support - Licensing and Entitlement Issues (Doc ID 1603494.2)
However there are benefits of licensing if you want to explore Oracle Cloud. Oracle customers who already own a license to PeopleSoft applications may use the Oracle Cloud to host instances of their licensed applications. There are no additional application license requirements for using Oracle Compute Cloud resources.
You can. No separate license is required for it. Just make sure your hardware is sufficient enough to host a DB and all the Web/App/Prcs scheduler domains.