Persistit, like all Titan storage backends, supports concurrent access. Have a look at the parallel unit tests and their performance to get a feel for the exact performance characteristics.
However, note that Persistit will be moved out of the main Titan codebase into an experimental repository due to the recent lack of development on the project until further notice. I'd encourage you to consider using a single/embedded instance of Cassandra or BDB instead in the near future.