The answer to your question really depends upon the 'Connectivity' of your database. You can traverse ~1 million edges a second. So if your 3 degree hop needs to traverse most of your data it will be very slow, however if it needs to traverse only a few nodes it will be quick.
Think of it like sitting in a football stadium. If your 3 hops are 'who' is sitting within 3 seats of you, you don't have many nodes to traverse. However if your query is 'which Liverpool supporters, have a scarf and are dressed in red?', it will take a long time.
Also neo4j at the moment has a 32 bit address space for its nodes and edges, so you might run out of space with your billions of nodes.
Hope this helps