Setting up streaming replication with new server as master?

We would like to start using streaming replication, but the catch is that we want the new server to be the master. The server is still in use and receiving new data, so we would like to minimize down time, and I would prefer to be able to copy all, or at least the large majority of the data to the new server before doing the final sync to make it the master.

Will pg_basebackup work?

Can it be run multiple times? (i.e. start it now to copy all of the data over the weekend and then a second time on Monday before doing the switch)