Yes, it is possible, but if you want to test BAPI, the only thing left for you is a full-blown installation and configuration project - I think we can safely exclude it or install IDES. The reason is that with all the free test disks that I know of, you get only a development environment, but not an ECC core with business logic, and BAPIs are part of the ECC core.
Take a look at http://www.consolut.net/en/s/sap-ides-access.html - they seem to offer free access to IDES, which may be sufficient for your purposes. If you want to install IDES on your own box, you need to be an SAP client or partner with a valid license - if you are, go to service.sap.com/ides and do not forget to buy Really Big Machine [tm].
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