It looks like neo4j is built to run on NoSQL, so I don't believe so, at least natively.
Additionally if you were able to develop a shim to convert the NoSQL requests to Unity3d there would be a performance hit - neo4j is built to expect NoSQL and will run its queries to be optimized on NoSQL vs anything else.
TL;DR - Anything is possible, but you don't want to do that here.